Hướng dẫn Giải Bài 63 (trang 33, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 63 (Trang 33 SGK Toán 9, Tập 1)

Bài 63 (Trang 33 SGK Toán 9, Tập 1): Rút gọn các biểu thức sau: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><msqrt><mfrac><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi></mfrac></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>ab</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mfrac><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi></mfrac><msqrt><mfrac><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi></mfrac></msqrt><mo> </mo><mo> </mo><mi>với</mi><mo> </mo><mi mathvariant="normal">a</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn><mo> </mo><mi>và</mi><mo> </mo><mi mathvariant="normal">b</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><mfrac><mi mathvariant="normal">m</mi><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mrow></mfrac></msqrt><mo>.</mo><msqrt><mfrac><mrow><mn>4</mn><mi mathvariant="normal">m</mi><mo> </mo><mo>-</mo><mo> </mo><mn>8</mn><mi>mx</mi><mo> </mo><mo>+</mo><mo> </mo><mn>4</mn><msup><mi>mx</mi><mn>2</mn></msup></mrow><mn>81</mn></mfrac></msqrt><mo> </mo><mi>v</mi><mi>ớ</mi><mi>i</mi><mo> </mo><mi>m</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn><mo> </mo><mi>v</mi><mi>à</mi><mo> </mo><mi>x</mi><mo> </mo><mo>≠</mo><mn>1</mn><mo>.</mo></math>   Hướng dẫn giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><msqrt><mfrac><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi></mfrac></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>ab</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mfrac><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi></mfrac><msqrt><mfrac><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mfrac><mrow><mi mathvariant="normal">a</mi><mo>.</mo><mi mathvariant="normal">b</mi></mrow><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></mfrac></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>ab</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mfrac><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi></mfrac><msqrt><mfrac><mi>ab</mi><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup></mfrac></msqrt><mspace linebreak="newline"/><mo>=</mo><mo> </mo><mfrac><mn>1</mn><mi>b</mi></mfrac><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mfrac><mi>a</mi><mrow><mi>b</mi><mo>.</mo><mi>a</mi></mrow></mfrac><msqrt><mi>a</mi><mi>b</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mfrac><mn>1</mn><mi>b</mi></mfrac><mo>+</mo><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mi>b</mi></mfrac></mrow></mfenced><msqrt><mi>a</mi><mi>b</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mfrac><mn>2</mn><mi>b</mi></mfrac><mo>+</mo><mn>1</mn></mrow></mfenced><msqrt><mi>a</mi><mi>b</mi></msqrt></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><msqrt><mfrac><mi mathvariant="normal">m</mi><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mrow></mfrac></msqrt><mo> </mo><mo>.</mo><msqrt><mfrac><mrow><mn>4</mn><mi mathvariant="normal">m</mi><mo> </mo><mo>-</mo><mo> </mo><mo> </mo><mn>8</mn><mi>mx</mi><mo> </mo><mo>+</mo><mo> </mo><mn>4</mn><msup><mi>mx</mi><mn>2</mn></msup></mrow><mn>81</mn></mfrac></msqrt><mo>=</mo><mo> </mo><msqrt><mfrac><mi mathvariant="normal">m</mi><msup><mfenced><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">x</mi></mrow></mfenced><mn>2</mn></msup></mfrac></msqrt><mo>.</mo><msqrt><mfrac><mrow><mn>4</mn><mfenced><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mrow></mfenced></mrow><mn>81</mn></mfrac></msqrt><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo> </mo><msqrt><mfrac><mi mathvariant="normal">m</mi><msup><mfenced><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">x</mi></mrow></mfenced><mn>2</mn></msup></mfrac><mo>.</mo><mfrac><mrow><mn>4</mn><mi mathvariant="normal">m</mi><msup><mfenced><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">x</mi></mrow></mfenced><mi mathvariant="normal">x</mi></msup></mrow><mn>81</mn></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></mrow><mn>81</mn></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><msqrt><mn>4</mn><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></msqrt><msqrt><mn>81</mn></msqrt></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">m</mi></mrow><mn>9</mn></mfrac><mo> </mo><mo>(</mo><mi>v</mi><mi>ớ</mi><mi>i</mi><mo> </mo><mi>m</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn><mo> </mo><mi>v</mi><mi>à</mi><mo> </mo><mi>x</mi><mo> </mo><mo>≠</mo><mo> </mo><mn>1</mn><mo>)</mo></math>