Bài 1: Bất phương trình bậc nhất hai ẩn
Lý thuyết Bất phương trình bậc nhất hai ẩn
<h2><strong>1. Khái niệm bất phương trình bậc nhất hai ẩn</strong></h2>
<p>+) Bất phương trình bậc nhất hai ẩn x, y là BPT có một trong các dạng</p>
<p><span id="MathJax-Element-1-Frame" class="mjx-full-width mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 22.925em; min-height: 0px; border: 0px; width: 10000em; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>c</mi><mo>&#x2264;</mo><mn>0</mn><mspace width="thickmathspace" /><mo>;</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>c</mi><mo>&#x2265;</mo><mn>0</mn><mo>;</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>c</mi><mo>&lt;</mo><mn>0</mn><mo>;</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>c</mi><mo>&gt;</mo><mn>0</mn></math>"><span id="MJXc-Node-1" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-2" class="mjx-mrow"><span class="mjx-stack"><span class="mjx-block"><span class="mjx-box"><span id="MJXc-Node-3" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-4" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-5" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-6" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-7" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span><span id="MJXc-Node-8" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-9" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-10" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">≤</span></span><span id="MJXc-Node-11" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span><span id="MJXc-Node-12" class="mjx-mspace"></span><span id="MJXc-Node-13" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">; a</span></span><span id="MJXc-Node-15" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-16" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-17" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-18" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span><span id="MJXc-Node-19" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-20" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-21" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">≥</span></span><span id="MJXc-Node-22" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span><span id="MJXc-Node-23" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">; </span></span><span id="MJXc-Node-24" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-25" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-26" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-27" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-28" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span><span id="MJXc-Node-29" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-30" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-31" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"><</span></span><span id="MJXc-Node-32" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span><span id="MJXc-Node-33" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">; </span></span><span id="MJXc-Node-34" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-35" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span></span><span class="mjx-block"><span class="mjx-box"><span id="MJXc-Node-36" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-37" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-38" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span><span id="MJXc-Node-39" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-40" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-41" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">></span></span><span id="MJXc-Node-42" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span></span></span></span></p>
<p>trong đó a, b, c là những số cho trước, a và b không đồng thời bằng 0, x và y là các ẩn.</p>
<p>Ví dụ: <span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>&#x2212;</mo><mn>10</mn><mo>&gt;</mo><mn>0</mn></math>"><span id="MJXc-Node-43" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-44" class="mjx-mrow"><span id="MJXc-Node-45" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-46" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-47" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-48" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">3</span></span><span id="MJXc-Node-49" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span><span id="MJXc-Node-50" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">−</span></span><span id="MJXc-Node-51" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">10</span></span><span id="MJXc-Node-52" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">></span></span><span id="MJXc-Node-53" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span></p>
<h2><strong>2. Nghiệm của bất phương trình bậc nhất hai ẩn</strong></h2>
<p>+) Mỗi cặp số <span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>x</mi><mn>0</mn></msub></mrow><mo>;</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>y</mi><mn>0</mn></msub></mrow><mo stretchy="false">)</mo></math>"><span id="MJXc-Node-54" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-55" class="mjx-mrow"><span id="MJXc-Node-56" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-57" class="mjx-texatom"><span id="MJXc-Node-58" class="mjx-mrow"><span id="MJXc-Node-59" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-60" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-61" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-62" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-63" class="mjx-texatom MJXc-space1"><span id="MJXc-Node-64" class="mjx-mrow"><span id="MJXc-Node-65" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-66" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-67" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-68" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span></span></span> thỏa mãn <span id="MathJax-Element-4-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>x</mi><mn>0</mn></msub></mrow><mo>+</mo><mi>b</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>y</mi><mn>0</mn></msub></mrow><mo>+</mo><mi>c</mi><mspace width="thickmathspace" /><mo>&lt;</mo><mn>0</mn></math>"><span id="MJXc-Node-69" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-70" class="mjx-mrow"><span id="MJXc-Node-71" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-72" class="mjx-texatom"><span id="MJXc-Node-73" class="mjx-mrow"><span id="MJXc-Node-74" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-75" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-76" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-77" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-78" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-79" class="mjx-texatom"><span id="MJXc-Node-80" class="mjx-mrow"><span id="MJXc-Node-81" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-82" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-83" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-84" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-85" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-86" class="mjx-mspace"></span><span id="MJXc-Node-87" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"><</span></span><span id="MJXc-Node-88" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span> được gọi là một <strong>nghiệm</strong> của BPT đã cho.</p>
<p>Ví dụ: cặp số <span id="MathJax-Element-5-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mn>3</mn><mo>;</mo><mn>5</mn><mo stretchy="false">)</mo></math>"><span id="MJXc-Node-89" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-90" class="mjx-mrow"><span id="MJXc-Node-91" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-92" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">3</span></span><span id="MJXc-Node-93" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-94" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">5</span></span><span id="MJXc-Node-95" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span></span></span> là một nghiệm của BPT <span id="MathJax-Element-6-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>&#x2212;</mo><mn>10</mn><mo>&gt;</mo><mn>0</mn></math>"><span id="MJXc-Node-96" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-97" class="mjx-mrow"><span id="MJXc-Node-98" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-99" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-100" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-101" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">3</span></span><span id="MJXc-Node-102" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span><span id="MJXc-Node-103" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">−</span></span><span id="MJXc-Node-104" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">10</span></span><span id="MJXc-Node-105" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">></span></span><span id="MJXc-Node-106" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span> vì <span id="MathJax-Element-7-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.3</mn><mo>+</mo><mn>3.5</mn><mo>&#x2212;</mo><mn>10</mn><mo>=</mo><mn>11</mn><mo>&gt;</mo><mn>0</mn></math>"><span id="MJXc-Node-107" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-108" class="mjx-mrow"><span id="MJXc-Node-109" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">2.3</span></span><span id="MJXc-Node-110" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-111" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">3.5</span></span><span id="MJXc-Node-112" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">−</span></span><span id="MJXc-Node-113" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">10</span></span><span id="MJXc-Node-114" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-115" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">11</span></span><span id="MJXc-Node-116" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">></span></span><span id="MJXc-Node-117" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span></p>
<p>+) BPT bậc nhất hai ẩn luôn có <em><strong>vô số nghiệm</strong></em>.</p>
<h2><strong>3. Biểu diễn miền nghiệm của bất phương trình bậc nhất hai ẩn</strong></h2>
<p>+) Trong mặt phẳng tọa độ Oxy, tập hợp các điểm <span id="MathJax-Element-8-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>x</mi><mn>0</mn></msub></mrow><mo>;</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>y</mi><mn>0</mn></msub></mrow><mo stretchy="false">)</mo></math>"><span id="MJXc-Node-118" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-119" class="mjx-mrow"><span id="MJXc-Node-120" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-121" class="mjx-texatom"><span id="MJXc-Node-122" class="mjx-mrow"><span id="MJXc-Node-123" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-124" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-125" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-126" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-127" class="mjx-texatom MJXc-space1"><span id="MJXc-Node-128" class="mjx-mrow"><span id="MJXc-Node-129" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-130" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-131" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-132" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span></span></span> sao cho <span id="MathJax-Element-9-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>x</mi><mn>0</mn></msub></mrow><mo>+</mo><mi>b</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>y</mi><mn>0</mn></msub></mrow><mo>+</mo><mi>c</mi><mo>&lt;</mo><mn>0</mn></math>"><span id="MJXc-Node-133" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-134" class="mjx-mrow"><span id="MJXc-Node-135" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-136" class="mjx-texatom"><span id="MJXc-Node-137" class="mjx-mrow"><span id="MJXc-Node-138" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-139" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-140" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-141" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-142" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-143" class="mjx-texatom"><span id="MJXc-Node-144" class="mjx-mrow"><span id="MJXc-Node-145" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-146" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-147" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-148" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-149" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-150" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"><</span></span><span id="MJXc-Node-151" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span> được gọi là <strong>miền nghiệm</strong> của bất phương trình <span id="MathJax-Element-10-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>c</mi><mo>&lt;</mo><mn>0</mn></math>"><span id="MJXc-Node-152" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-153" class="mjx-mrow"><span id="MJXc-Node-154" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-155" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-156" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-157" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-158" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span><span id="MJXc-Node-159" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-160" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-161" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"><</span></span><span id="MJXc-Node-162" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span></p>
<p><strong>+) Biểu diễn miền nghiệm của BPT <span id="MathJax-Element-11-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.68px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>c</mi><mo>&lt;</mo><mn>0</mn></math>"><span id="MJXc-Node-163" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-164" class="mjx-mrow"><span id="MJXc-Node-165" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-166" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-167" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-168" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-169" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span><span id="MJXc-Node-170" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-171" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-172" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"><</span></span><span id="MJXc-Node-173" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span></strong></p>
<p>Bước 1: Trên mặt phẳng Oxy, vẽ đường thẳng <span id="MathJax-Element-12-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0394;</mi><mo>:</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math>"><span id="MJXc-Node-174" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-175" class="mjx-mrow"><span id="MJXc-Node-176" class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R">Δ</span></span><span id="MJXc-Node-177" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">:</span></span><span id="MJXc-Node-178" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-179" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-180" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-181" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-182" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span><span id="MJXc-Node-183" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-184" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-185" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-186" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span>.</p>
<p>Bước 2: Lấy một điểm <span id="MathJax-Element-13-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>x</mi><mn>0</mn></msub></mrow><mo>;</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>y</mi><mn>0</mn></msub></mrow><mo stretchy="false">)</mo></math>"><span id="MJXc-Node-187" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-188" class="mjx-mrow"><span id="MJXc-Node-189" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-190" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-191" class="mjx-texatom"><span id="MJXc-Node-192" class="mjx-mrow"><span id="MJXc-Node-193" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-194" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-195" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-196" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-197" class="mjx-texatom MJXc-space1"><span id="MJXc-Node-198" class="mjx-mrow"><span id="MJXc-Node-199" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-200" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-201" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">)</mo></math></span></span> không thuộc <span id="MathJax-Element-14-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0394;</mi><mo>.</mo></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi><mo>.</mo></math></span></span> Tính <span id="MathJax-Element-15-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>x</mi><mn>0</mn></msub></mrow><mo>+</mo><mi>b</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>y</mi><mn>0</mn></msub></mrow><mo>+</mo><mi>c</mi></math>"><span id="MJXc-Node-207" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-208" class="mjx-mrow"><span id="MJXc-Node-209" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-210" class="mjx-texatom"><span id="MJXc-Node-211" class="mjx-mrow"><span id="MJXc-Node-212" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-213" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-214" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-215" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-216" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-217" class="mjx-texatom"><span id="MJXc-Node-218" class="mjx-mrow"><span id="MJXc-Node-219" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-220" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-221" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-222" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-223" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span></span></span></span></p>
<p>Bước 3: Kết luận</p>
<p>- Nếu <span id="MathJax-Element-16-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>x</mi><mn>0</mn></msub></mrow><mo>+</mo><mi>b</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>y</mi><mn>0</mn></msub></mrow><mo>+</mo><mi>c</mi><mo>&lt;</mo><mn>0</mn></math>"><span id="MJXc-Node-224" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-225" class="mjx-mrow"><span id="MJXc-Node-226" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-227" class="mjx-texatom"><span id="MJXc-Node-228" class="mjx-mrow"><span id="MJXc-Node-229" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-230" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-231" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-232" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-233" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-234" class="mjx-texatom"><span id="MJXc-Node-235" class="mjx-mrow"><span id="MJXc-Node-236" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-237" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-238" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-239" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-240" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-241" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"><</span></span><span id="MJXc-Node-242" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span> thì miền nghiệm của bất phương trình đã cho là nửa mặt phẳng (không kể bờ <span id="MathJax-Element-17-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0394;</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi></math></span></span>) chứa điểm <span id="MathJax-Element-18-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></span></span>.</p>
<p>- Nếu <span id="MathJax-Element-19-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>x</mi><mn>0</mn></msub></mrow><mo>+</mo><mi>b</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>y</mi><mn>0</mn></msub></mrow><mo>+</mo><mi>c</mi><mo>&gt;</mo><mn>0</mn></math>"><span id="MJXc-Node-249" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-250" class="mjx-mrow"><span id="MJXc-Node-251" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-252" class="mjx-texatom"><span id="MJXc-Node-253" class="mjx-mrow"><span id="MJXc-Node-254" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-255" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-256" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-257" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-258" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">b</span></span><span id="MJXc-Node-259" class="mjx-texatom"><span id="MJXc-Node-260" class="mjx-mrow"><span id="MJXc-Node-261" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-262" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span><sub><span class="mjx-sub"><span id="MJXc-Node-263" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></sub></span></span></span><span id="MJXc-Node-264" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">+</span></span><span id="MJXc-Node-265" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-266" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">></span></span><span id="MJXc-Node-267" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span> thì miền nghiệm của bất phương trình đã cho là nửa mặt phẳng (không kể bờ <span id="MathJax-Element-20-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0394;</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi></math></span></span>) không chứa điểm <span id="MathJax-Element-21-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></span></span>.</p>
<p><strong>* Chú ý:</strong></p>
<p>- Nếu <span id="MathJax-Element-22-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>&#x2260;</mo><mn>0</mn></math>"><span id="MJXc-Node-274" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-275" class="mjx-mrow"><span id="MJXc-Node-276" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-277" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">≠</span></span><span id="MJXc-Node-278" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span> ta thường chọn <span id="MathJax-Element-23-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math>"><span id="MJXc-Node-279" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-280" class="mjx-mrow"><span id="MJXc-Node-281" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span></span> là gốc tọa độ.</p>
<p>- Nếu <span id="MathJax-Element-24-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math>"><span id="MJXc-Node-282" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-283" class="mjx-mrow"><span id="MJXc-Node-284" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-285" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-286" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">0</span></span></span></span></span> ta thường chọn <span id="MathJax-Element-25-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></span></span> có tọa độ <span id="MathJax-Element-26-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mn>1</mn><mo>;</mo><mn>0</mn><mo stretchy="false">)</mo></math>"><span id="MJXc-Node-290" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-291" class="mjx-mrow"><span id="MJXc-Node-292" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-293" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">1</span></span><span id="MJXc-Node-294" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-295" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">0</span></span><span id="MJXc-Node-296" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span></span></span> hoặc <span id="MathJax-Element-27-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.36px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mn>0</mn><mo>;</mo><mn>1</mn><mo stretchy="false">)</mo><mo>.</mo></math>"><span id="MJXc-Node-297" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-298" class="mjx-mrow"><span id="MJXc-Node-299" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-300" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">0</span></span><span id="MJXc-Node-301" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-302" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">1</span></span><span id="MJXc-Node-303" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span><span id="MJXc-Node-304" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">.</span></span></span></span></span></p>
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