Hướng dẫn Giải Bài 53 (trang 30, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 53 (Trang 30 SGK Toán 9, Tập 1)

Bài 53 (Trang 30 SGK Toán 9, Tập 1) Rút gọn các biểu thức sau (giả thiết các biểu thức chữ đều có nghĩa) : a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>18</mn><msup><mrow><mo>(</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow><mn>2</mn></msup></msqrt><mo>;</mo></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><msqrt><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mrow><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></mrow></mfrac></msqrt></math>; c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mi mathvariant="normal">a</mi><msup><mi mathvariant="normal">b</mi><mn>3</mn></msup></mfrac><mo>+</mo><mfrac><mi mathvariant="normal">a</mi><msup><mi mathvariant="normal">b</mi><mn>4</mn></msup></mfrac></msqrt></math>;  d) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi mathvariant="normal">a</mi><mo>+</mo><msqrt><mi>ab</mi></msqrt></mrow><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfrac></math>.   Hướng dẫn giải: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>18</mn><msup><mrow><mo>(</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced open="|" close="|"><mrow><msqrt><mn>2</mn></msqrt><mo>-</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><msqrt><mn>2</mn><mo>.</mo><mn>9</mn></msqrt></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>)</mo><mo>.</mo><msqrt><mn>2</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>)</mo><msqrt><mn>2</mn></msqrt></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><msqrt><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mrow><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></mrow></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mi>ab</mi><msqrt><mfrac><mrow><mn>1</mn><mo>+</mo><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></mrow><mrow><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></mrow></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi>ab</mi><mfenced open="|" close="|"><mi>ab</mi></mfenced></mfrac><msqrt><mn>1</mn><mo>+</mo><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></msqrt></math>    <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msqrt><mn>1</mn><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup><msup><mi>b</mi><mn>2</mn></msup></msqrt><mo> </mo><mi>n</mi><mi>ế</mi><mi>u</mi><mo> </mo><mi>a</mi><mi>b</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn><mo> </mo></mtd></mtr><mtr><mtd><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup><msup><mi>b</mi><mn>2</mn></msup></msqrt><mo> </mo><mi>n</mi><mi>ế</mi><mi>u</mi><mo> </mo><mi>a</mi><mi>b</mi><mo> </mo><mo><</mo><mo> </mo><mn>0</mn></mtd></mtr></mtable></mfenced></math> c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mi mathvariant="normal">a</mi><msup><mi mathvariant="normal">b</mi><mn>3</mn></msup></mfrac><mo>+</mo><mfrac><mi mathvariant="normal">a</mi><msup><mi mathvariant="normal">b</mi><mn>4</mn></msup></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mfrac><mrow><mi mathvariant="normal">a</mi><mo>+</mo><mi>ab</mi></mrow><msup><mi mathvariant="normal">b</mi><mn>4</mn></msup></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>1</mn><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></mfrac><msqrt><mi mathvariant="normal">a</mi><mo>+</mo><mi>ab</mi></msqrt><mo>;</mo></math> d) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi mathvariant="normal">a</mi><mo>+</mo><msqrt><mi>ab</mi></msqrt></mrow><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mo>(</mo><mi mathvariant="normal">a</mi><mo>+</mo><msqrt><mi>ab</mi></msqrt><mo>)</mo><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>-</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo></mrow><mrow><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>-</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mi mathvariant="normal">a</mi><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>-</mo><mi mathvariant="normal">a</mi><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>+</mo><mi mathvariant="normal">a</mi><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>-</mo><mi mathvariant="normal">b</mi><msqrt><mi mathvariant="normal">a</mi></msqrt></mrow><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfrac></math>    =<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>a</mi><msqrt><mi>a</mi></msqrt><mo>-</mo><mi>b</mi><msqrt><mi>a</mi></msqrt></mrow><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><msqrt><mi>a</mi></msqrt></mrow><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><msqrt><mi>a</mi></msqrt><mo>;</mo></math> Cách khác: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi mathvariant="normal">a</mi><mo>+</mo><msqrt><mi>ab</mi></msqrt></mrow><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><msup><mrow><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>.</mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo></mrow><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>.</mo></math>