Hướng dẫn giải Bài 16 (Trang 133 SGK Toán Đại số 9, Tập 2)

Giải các phương trình: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>0</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>12</mn></math> Giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>0</mn><mspace linebreak="newline"/><mo>⇔</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>0</mn><mspace linebreak="newline"/><mo>⇔</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mn>3</mn><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>6</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mspace linebreak="newline"/><mo>⇔</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>⇔</mo><mo>[</mo><mtable><mtr><mtd><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>0</mn></mtd></mtr></mtable></math> Giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn><mo> </mo></math>được <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn></math> Giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>0</mn></math>, vô nghiệm Vậy phương trình đã cho có một nghiệm <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>)</mo><mo> </mo><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>12</mn><mspace linebreak="newline"/><mo>⇔</mo><mfenced open="[" close="]"><mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfenced><mfenced open="[" close="]"><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mn>12</mn><mspace linebreak="newline"/><mo>⇔</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mi>x</mi></mrow></mfenced><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>=</mo><mn>12</mn></math> Đặt <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn><mo>=</mo><mi>y</mi></math> ta có:<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>y</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>12</mn><mo>⇔</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>16</mn><mo>⇔</mo><mi>y</mi><mo>=</mo><mo>±</mo><mn>4</mn></math> - Với <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>4</mn></math>, giải được <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn><mo>=</mo><mn>4</mn><mo>⇒</mo><msub><mi>x</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>-</mo><mn>5</mn><mo>±</mo><msqrt><mn>33</mn></msqrt></mrow><mn>2</mn></mfrac></math> - Với <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn></math>, giải được <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn><mo>=</mo><mo>-</mo><mn>4</mn><mo>⇒</mo><msub><mi>x</mi><mn>3</mn></msub><mo>=</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo> </mo><msub><mi>x</mi><mn>4</mn></msub><mo>=</mo><mo>-</mo><mn>3</mn></math> Vậy tập nghiệm <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mfenced open="{" close="}"><mrow><mo>-</mo><mn>2</mn><mo>;</mo><mo>-</mo><mn>3</mn><mo>;</mo><mfrac><mrow><mo>-</mo><mn>5</mn><mo>±</mo><msqrt><mn>33</mn></msqrt></mrow><mn>2</mn></mfrac></mrow></mfenced></math>

Hướng dẫn Giải Bài 16, Phần Đại số (Trang 133, SGK Toán 9, Tập 2)

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