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

Giải các hệ phương trình: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mfenced open="|" close="|"><mi>y</mi></mfenced><mo>=</mo><mn>13</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>;</mo><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>3</mn><msqrt><mi>x</mi></msqrt><mo>-</mo><mn>2</mn><msqrt><mi>y</mi></msqrt><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><msqrt><mi>y</mi></msqrt><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math> Giải:  a) Trường hợp <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>≥</mo><mn>0</mn></math> hệ đã cho trở thành <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>13</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>13</mn></mtd></mtr><mtr><mtd><mn>9</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>11</mn><mi>x</mi><mo>=</mo><mn>22</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>13</mn></mtd></mtr></mtable></mfenced><mspace linebreak="newline"/><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>y</mi><mo>=</mo><mn>13</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math> Trường hợp <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo><</mo><mn>0</mn></math> hệ đã cho trở thành <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>13</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>13</mn></mtd></mtr><mtr><mtd><mn>9</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>7</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>9</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mspace linebreak="newline"/><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>4</mn><mn>7</mn></mfrac></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>9</mn><mo>-</mo><mn>9</mn><mfenced><mrow><mo>-</mo><mfrac><mn>4</mn><mn>7</mn></mfrac></mrow></mfenced></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>4</mn><mn>7</mn></mfrac></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mfrac><mn>99</mn><mn>7</mn></mfrac></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>4</mn><mn>7</mn></mfrac></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>33</mn><mn>7</mn></mfrac></mtd></mtr></mtable></mfenced></math> Vậy: Trường hợp <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>≥</mo><mn>0</mn></math>, hệ có nghiệm <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo> </mo><mi>y</mi><mo>=</mo><mn>3</mn></math>. Trường hợp <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo><</mo><mn>0</mn></math>, hệ có nghiệm <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>4</mn><mn>7</mn></mfrac><mo>,</mo><mo> </mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>33</mn><mn>7</mn></mfrac></math> b) Đặt <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>x</mi></msqrt><mo>=</mo><mi>X</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mo> </mo><msqrt><mi>y</mi></msqrt><mo>=</mo><mi>Y</mi><mo>≥</mo><mn>0</mn></math> ta được hệ: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>3</mn><mi>X</mi><mo>-</mo><mn>2</mn><mi>Y</mi><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>X</mi><mo>+</mo><mi>Y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>3</mn><mi>X</mi><mo>-</mo><mn>2</mn><mi>Y</mi><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>4</mn><mi>X</mi><mo>+</mo><mn>2</mn><mi>Y</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>7</mn><mi>X</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>Y</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>X</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>Y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mspace linebreak="newline"/><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><msqrt><mi>x</mi></msqrt><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><msqrt><mi>y</mi></msqrt><mo>=</mo><mn>1</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math>

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

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