Bài 5: Công thức nghiệm thu gọn
Hướng dẫn giải Bài 17 (Trang 49 SGK Toán Đại số 9, Tập 2)
<p>Xác định a, b', c rồi dùng công thức nghiệm thu gọn giải các phương trình:</p>
<p>a) 4x<sup>2</sup>+4x+1=0<span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span>b) 13852x<sup>2 </sup>- 14x+1=0</p>
<p>c) 5x<sup>2</sup> - 6x+1=0<span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span>d) -3x<sup>2</sup>+<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msqrt><mn>6</mn></msqrt></math>x+4=0</p>
<p><strong>Giải:</strong></p>
<p>a) 4x<sup>2</sup>+4x+1=0 có a=4, b=4, b'=2, c=1</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mo>'</mo><mo>=</mo><msup><mn>2</mn><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>.</mo><mn>1</mn><mo>=</mo><mn>0</mn><mo>:</mo><mo> </mo><mi>Phương</mi><mo> </mo><mi>trình</mi><mo> </mo><mi>có</mi><mo> </mo><mi>nghiệm</mi><mo> </mo><mi>kép</mi><mo>.</mo><mspace linebreak="newline"/><msub><mi mathvariant="normal">x</mi><mn>1</mn></msub><mo>=</mo><msub><mi mathvariant="normal">x</mi><mn>2</mn></msub><mo>=</mo><mo>-</mo><mfrac><mn>2</mn><mn>4</mn></mfrac><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></p>
<p>b) 13852x<sup>2</sup>-14x+1=0 có a=13852, b=-14, b'=-7, c=1</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mo>'</mo><mo>=</mo><msup><mfenced><mrow><mo>-</mo><mn>7</mn></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>13852</mn><mo>.</mo><mn>1</mn><mo>=</mo><mn>49</mn><mo>-</mo><mn>13852</mn><mo><</mo><mn>0</mn><mspace linebreak="newline"/><mi>Phương</mi><mo> </mo><mi>trình</mi><mo> </mo><mi>vô</mi><mo> </mo><mi>nghiệm</mi><mo>.</mo></math></p>
<p>c) 5x<sup>2</sup> - 6x+1=0 có a=5, b=-6, c=1</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mo>'</mo><mo>=</mo><msup><mrow><mo>(</mo><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>=</mo><mn>4</mn><mo>,</mo><mo> </mo><msqrt><mo>∆</mo><mo>'</mo></msqrt><mo>=</mo><mn>2</mn><mspace linebreak="newline"/><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mn>3</mn><mo>+</mo><mn>2</mn></mrow><mn>5</mn></mfrac><mo>=</mo><mn>1</mn><mo>,</mo><mo> </mo><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mn>3</mn><mo>-</mo><mn>2</mn></mrow><mn>5</mn></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></math></p>
<p>d) </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msqrt><mn>6</mn></msqrt><mi>x</mi><mo>+</mo><mn>4</mn><mo>=</mo><mn>0</mn><mo> </mo><mi>c</mi><mi>ó</mi><mo> </mo><mi>a</mi><mo>=</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>4</mn><msqrt><mn>6</mn></msqrt><mo>,</mo><mo> </mo><mi>b</mi><mo>'</mo><mo>=</mo><mn>2</mn><msqrt><mn>6</mn></msqrt><mo>,</mo><mo> </mo><mi>c</mi><mo>=</mo><mn>4</mn><mspace linebreak="newline"/><mo>∆</mo><mo>'</mo><mo>=</mo><msup><mrow><mo>(</mo><mn>2</mn><msqrt><mn>6</mn></msqrt><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>)</mo><mo>.</mo><mn>4</mn><mo>=</mo><mn>24</mn><mo>+</mo><mn>12</mn><mo>=</mo><mn>36</mn><mo>,</mo><mo> </mo><msqrt><mo>∆</mo><mo>'</mo></msqrt><mo>=</mo><mn>6</mn><mspace linebreak="newline"/><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><msqrt><mn>6</mn></msqrt><mo>+</mo><mn>6</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><msqrt><mn>6</mn></msqrt><mo>-</mo><mn>6</mn></mrow><mn>3</mn></mfrac><mo>;</mo><mo> </mo><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><msqrt><mn>6</mn></msqrt><mo>-</mo><mn>6</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><msqrt><mn>6</mn></msqrt><mo>+</mo><mn>6</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></mfrac></math></p>
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