Bài 4: Giải hệ phương trình bằng phương pháp cộng đại số
Hướng dẫn giải Bài 21 (Trang 19 SGK Toán Đại số 9, Tập 2)
<p>Giải c&aacute;c hệ phương tr&igrave;nh sau bằng phương ph&aacute;p cộng đại số:</p> <p>a,<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi><msqrt><mn>2</mn></msqrt><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math>;&nbsp; &nbsp; &nbsp; b, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>5</mn><mi>x</mi><msqrt><mn>3</mn></msqrt><mo>+</mo><mi>y</mi><mo>=</mo><mn>2</mn><msqrt><mn>2</mn></msqrt></mtd></mtr><mtr><mtd><mi>x</mi><msqrt><mn>6</mn></msqrt><mo>-</mo><mi>y</mi><msqrt><mn>2</mn></msqrt><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></p> <p>Giải:&nbsp;</p> <p>a, Nh&acirc;n phương tr&igrave;nh thứ nhất với -<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math>, ta được:</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi><msqrt><mn>2</mn></msqrt><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt><mi>y</mi><mo>=</mo><mo>-</mo><msqrt><mn>2</mn></msqrt></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi><msqrt><mn>2</mn></msqrt><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>4</mn><msqrt><mn>2</mn></msqrt><mi>y</mi><mo>=</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi><msqrt><mn>2</mn></msqrt><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>-</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac><mi>y</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mn>2</mn></msqrt></mrow><mn>4</mn></mfrac></mtd></mtr></mtable><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mn>3</mn></mrow><mn>4</mn></mfrac><mo>+</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>8</mn></mfrac></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mn>4</mn></mfrac><mo>-</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>4</mn></mfrac></mtd></mtr></mtable></mfenced></mrow></mfenced></math></p> <p>b, Nh&acirc;n phương tr&igrave;nh thứ nhất với&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math> rồi cộng từng vế hai phương tr&igrave;nh ta được:&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mi>x</mi><msqrt><mn>6</mn></msqrt><mo>+</mo><mi>x</mi><msqrt><mn>6</mn></msqrt><mo>=</mo><mn>6</mn><mo>&#8660;</mo><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>6</mn></msqrt></mfrac></math></p> <p>Từ đ&oacute; hệ đ&atilde; cho tương đương với&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>6</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mi>x</mi><msqrt><mn>6</mn></msqrt><mo>-</mo><mi>y</mi><msqrt><mn>2</mn></msqrt><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>6</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac></mtd></mtr></mtable></mfenced></math></p> <p>&nbsp;</p>
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