Hướng dẫn giải Bài 10 (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><msqrt><mi>x</mi><mo>-</mo><mn>1</mn></msqrt><mo>-</mo><msqrt><mi>y</mi><mo>-</mo><mn>1</mn></msqrt><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><msqrt><mi>x</mi><mo>-</mo><mn>1</mn></msqrt><mo>+</mo><msqrt><mi>y</mi><mo>-</mo><mn>1</mn></msqrt><mo>=</mo><mn>2</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><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>3</mn><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math> Giải: a) Đặt <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>x</mi><mo>-</mo><mn>1</mn></msqrt><mo>=</mo><mi>X</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mo> </mo><msqrt><mi>y</mi><mo>-</mo><mn>1</mn></msqrt><mo>=</mo><mi>Y</mi><mo>≥</mo><mn>0</mn></math> Ta được: <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><mi>Y</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>X</mi><mo>+</mo><mi>Y</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>3</mn><mi>X</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>X</mi><mo>+</mo><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>1</mn></mtd></mtr><mtr><mtd><mi>Y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math> hay <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msqrt><mi>x</mi><mo>-</mo><mn>1</mn></msqrt><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><msqrt><mi>y</mi><mo>-</mo><mn>1</mn></msqrt><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>-</mo><mn>1</mn><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>-</mo><mn>1</mn><mo>=</mo><mn>1</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>2</mn></mtd></mtr></mtable></mfenced></math> b) Đặt <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mi>X</mi><mo>≥</mo><mn>0</mn></math> Ta được:  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>X</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>X</mi><mo>+</mo><mn>3</mn><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>6</mn><mi>y</mi><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>X</mi><mo>+</mo><mn>3</mn><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>6</mn><mi>y</mi><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>9</mn><mi>y</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mspace linebreak="newline"/><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>3</mn><mi>X</mi><mo>=</mo><mn>6</mn><mo>+</mo><mn>6</mn><mfenced><mrow><mo>-</mo><mfrac><mn>5</mn><mn>9</mn></mfrac></mrow></mfenced></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>5</mn><mn>9</mn></mfrac></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>X</mi><mo>=</mo><mfrac><mn>8</mn><mn>9</mn></mfrac></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>5</mn><mn>9</mn></mfrac></mtd></mtr></mtable></mfenced></math> Từ <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfrac><mn>8</mn><mn>9</mn></mfrac></math> ta được <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mfrac><mn>8</mn><mn>9</mn></mfrac><mo>⇔</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>=</mo><mo>±</mo><mfrac><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow><mn>3</mn></mfrac><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>1</mn><mo>±</mo><mfrac><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow><mn>3</mn></mfrac></math> Vậy hệ phương trình có nghiệm: <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow><mn>3</mn></mfrac><mo>;</mo><mo> </mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>5</mn><mn>9</mn></mfrac><mspace linebreak="newline"/><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mn>1</mn><mo>-</mo><mfrac><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow><mn>3</mn></mfrac><mo>;</mo><mo> </mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>5</mn><mn>9</mn></mfrac></math>

Hướng dẫn Giải Bài 10, Phần Đại số (Trang 133, SGK Toán 9, Tập 2)

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