Hướng dẫn giải Bài 76 (Trang 41 SGK Toán 9, Tập 1)

Bài 76 (Trang 41 SGK Toán 9, Tập 1): Cho biểu thức: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Q</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi mathvariant="normal">a</mi><msqrt><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo> </mo><mo>-</mo><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></msqrt></mfrac><mo> </mo><mo>-</mo><mo> </mo><mfenced><mrow><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><mfrac><mn>1</mn><msqrt><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo> </mo><mo>-</mo><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></msqrt></mfrac></mrow></mfenced><mo> </mo><mo>:</mo><mo> </mo><mfrac><mi mathvariant="normal">b</mi><msqrt><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo> </mo><mo>-</mo><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></msqrt></mfrac><mo> </mo><mi>v</mi><mi>ớ</mi><mi>i</mi><mo> </mo><mi>a</mi><mo> </mo><mo>></mo><mo> </mo><mi>b</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn><mo>.</mo></math> a) Rút gọn Q b) Xác định giá trị của Q khi a = 3b   Hướng dẫn giải: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Q</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi mathvariant="normal">a</mi><msqrt><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo>-</mo><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></msqrt></mfrac><mo> </mo><mo>-</mo><mo> </mo><mfenced><mrow><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><mfrac><mi mathvariant="normal">a</mi><msqrt><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo>-</mo><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></msqrt></mfrac></mrow></mfenced><mo> </mo><mo>:</mo><mo> </mo><mfrac><mi mathvariant="normal">b</mi><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mo> </mo><msqrt><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo>-</mo><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></msqrt></mrow></mfrac><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi>a</mi><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></mfrac><mo> </mo><mo>-</mo><mo> </mo><mfrac><mrow><mi>a</mi><mo>+</mo><msup><mfenced><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></mfenced><mn>2</mn></msup></mrow><mrow><mi>b</mi><mo>.</mo><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></mrow></mfrac><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mfrac><mi>a</mi><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></mfrac><mo> </mo><mo>-</mo><mo> </mo><mo> </mo><mfrac><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mo> </mo><mo>(</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup><mo>)</mo></mrow><mrow><mi>b</mi><mo>.</mo><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></mrow></mfrac><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mfrac><mi>a</mi><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></mfrac><mo>-</mo><mfrac><msup><mi>b</mi><mn>2</mn></msup><mrow><mi>b</mi><mo>.</mo><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></mrow></mfrac><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mfrac><mi>a</mi><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></mfrac><mo>-</mo><mfrac><mi>b</mi><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></mfrac><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><msqrt><msup><mfenced><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></msqrt><msqrt><mfenced><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow></mfenced><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></mfenced></msqrt></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><msqrt><mi>a</mi><mo>-</mo><mi>b</mi></msqrt><msqrt><mi>a</mi><mo>+</mo><mi>b</mi></msqrt></mfrac><mo>.</mo></math> b)  Thay a = 3b vào ta được: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>3</mn><mi>b</mi><mo>-</mo><mi>b</mi></msqrt><msqrt><mn>3</mn><mi>b</mi><mo>+</mo><mi>b</mi></msqrt></mfrac><mo> </mo><mo>=</mo><mfrac><msqrt><mn>2</mn><mi>b</mi></msqrt><msqrt><mn>4</mn><mi>b</mi></msqrt></mfrac><mo>=</mo><msqrt><mfrac><mn>1</mn><mn>2</mn></mfrac></msqrt><mo>=</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math>.