Hướng dẫn Giải Bài 72 (trang 40, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 72 (Trang 40 SGK Toán 9, Tập 1)

Bài 72 (Trang 40 SGK Toán 9, Tập 1): Phân tích thành nhân tử (với các số x, y, a, b không âm và a ≥ b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><mi>xy</mi><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">y</mi><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><msqrt><mi>ax</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi>by</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>bx</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi>ay</mi></msqrt><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>)</mo><mo> </mo><msqrt><mi mathvariant="normal">a</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">b</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo> </mo><mo>-</mo><mo> </mo><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></msqrt><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mn>12</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">x</mi><mo>.</mo></math>   Hướng dẫn giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><mi>xy</mi><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">y</mi><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><msup><mfenced><msqrt><mi mathvariant="normal">x</mi></msqrt></mfenced><mn>2</mn></msup><mo>.</mo><mi mathvariant="normal">y</mi><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">y</mi><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mspace linebreak="newline"/><mspace linebreak="newline"/><mo>=</mo><mo> </mo><mi mathvariant="normal">y</mi><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">y</mi><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mi mathvariant="normal">y</mi><msqrt><mi mathvariant="normal">x</mi></msqrt><mfenced><mrow><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn></mrow></mfenced><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn></mrow></mfenced><mo> </mo><mi>với</mi><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>≥</mo><mo> </mo><mn>0</mn><mo>.</mo></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><msqrt><mi>ax</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi>by</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>bx</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi>ay</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mi>ax</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi>bx</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>ay</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi>by</mi></msqrt><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mfenced><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfenced><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mfenced><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfenced><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt></mrow></mfenced><mspace linebreak="newline"/><mspace linebreak="newline"/><mo mathvariant="italic">(</mo><mi>V</mi><mi>ớ</mi><mi>i</mi><mo mathvariant="italic"> </mo><mi>x</mi><mo mathvariant="italic">,</mo><mo mathvariant="italic"> </mo><mi>y</mi><mo mathvariant="italic">,</mo><mo mathvariant="italic"> </mo><mi>a</mi><mo mathvariant="italic">,</mo><mo mathvariant="italic"> </mo><mi>b</mi><mo mathvariant="italic"> </mo><mi>đ</mi><mi>ề</mi><mi>u</mi><mo mathvariant="italic"> </mo><mi>k</mi><mi>h</mi><mi>ô</mi><mi>n</mi><mi>g</mi><mo mathvariant="italic"> </mo><mi>â</mi><mi>m</mi><mo mathvariant="italic">)</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>)</mo><mo> </mo><msqrt><mi mathvariant="normal">a</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">b</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo> </mo><mo>-</mo><mo> </mo><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mi mathvariant="normal">a</mi><mo> </mo><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">b</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mfenced><mrow><mi mathvariant="normal">a</mi><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">b</mi></mrow></mfenced><mfenced><mrow><mi mathvariant="normal">a</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">b</mi></mrow></mfenced></msqrt><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo> </mo><msqrt><mi mathvariant="normal">a</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">b</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">a</mi><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">b</mi></msqrt><mo>.</mo><msqrt><mi mathvariant="normal">a</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">b</mi></msqrt><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo> </mo><msqrt><mi mathvariant="normal">a</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">b</mi></msqrt><mfenced><mrow><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">a</mi><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">b</mi></msqrt></mrow></mfenced><mspace linebreak="newline"/><mspace linebreak="newline"/><mo mathvariant="italic">(</mo><mi>V</mi><mi>ớ</mi><mi>i</mi><mo mathvariant="italic"> </mo><mi>a</mi><mo mathvariant="italic"> </mo><mo mathvariant="italic">+</mo><mo mathvariant="italic"> </mo><mi>b</mi><mo mathvariant="italic">,</mo><mo mathvariant="italic"> </mo><mi>a</mi><mo mathvariant="italic"> </mo><mo mathvariant="italic">-</mo><mo mathvariant="italic"> </mo><mi>b</mi><mo mathvariant="italic"> </mo><mi>k</mi><mi>h</mi><mi>ô</mi><mi>n</mi><mi>g</mi><mo mathvariant="italic"> </mo><mi>â</mi><mi>m</mi><mo mathvariant="italic">)</mo></math> <div class="ads_ads ads_1"> </div> <div class="ads_ads ads_1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mn>12</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>16</mn><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><mn>4</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced open="[" close="]"><mrow><msup><mn>4</mn><mn>2</mn></msup><mo> </mo><mo>-</mo><mo> </mo><msup><mfenced><msqrt><mi mathvariant="normal">x</mi></msqrt></mfenced><mn>2</mn></msup></mrow></mfenced><mo> </mo><mo>-</mo><mo> </mo><mfenced><mrow><mn>4</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt></mrow></mfenced><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mn>4</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt></mrow></mfenced><mfenced><mrow><mn>4</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt></mrow></mfenced><mo> </mo><mo>-</mo><mo> </mo><mfenced><mrow><mn>4</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt></mrow></mfenced><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mn>4</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt></mrow></mfenced><mfenced><mrow><mn>4</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn></mrow></mfenced><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mn>4</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi></msqrt></mrow></mfenced><mo>.</mo></math></div>