Hướng dẫn Giải Bài 49 (trang 29, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 49 (Trang 29 SGK Toán 9, Tập 1)

Bài 49 (Trang 29 SGK Toán 9, Tập 1): Khử mẫu của biểu thức lấy căn: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>b</mi><msqrt><mfrac><mi>a</mi><mi>b</mi></mfrac></msqrt><mo>;</mo><mo> </mo><mfrac><mi>a</mi><mi>b</mi></mfrac><msqrt><mfrac><mi>b</mi><mi>a</mi></mfrac></msqrt><mo>;</mo><mo> </mo><msqrt><mfrac><mn>1</mn><mi>b</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><msup><mi>b</mi><mn>2</mn></msup></mfrac></msqrt><mo>;</mo><mo> </mo><msqrt><mfrac><mrow><mn>9</mn><msup><mi>a</mi><mn>3</mn></msup></mrow><mrow><mn>36</mn><mi>b</mi></mrow></mfrac></msqrt><mo>;</mo><mo> </mo><mn>3</mn><mi>x</mi><mi>y</mi><msqrt><mfrac><mn>2</mn><mrow><mi>x</mi><mi>y</mi></mrow></mfrac></msqrt><mo>.</mo></math> (Giả thiết các biểu thức có nghĩa).   Hướng dẫn giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><msqrt><mfrac><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mi>ab</mi><msqrt><mfrac><mi>ab</mi><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi>ab</mi><mfenced open="|" close="|"><mi mathvariant="normal">b</mi></mfenced></mfrac><msqrt><mi>ab</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">a</mi><msqrt><mi>ab</mi></msqrt><mo> </mo><mi>nếu</mi><mo> </mo><mi mathvariant="normal">b</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mi mathvariant="normal">a</mi><msqrt><mi>ab</mi></msqrt><mo> </mo><mi>nếu</mi><mo> </mo><mi mathvariant="normal">b</mi><mo> </mo><mo><</mo><mo> </mo><mn>0</mn></mtd></mtr></mtable></mfenced></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi></mfrac><msqrt><mfrac><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi></mfrac></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><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi mathvariant="normal">a</mi><mrow><mi mathvariant="normal">b</mi><mfenced open="|" close="|"><mi mathvariant="normal">a</mi></mfenced></mrow></mfrac><msqrt><mi>ab</mi></msqrt><mo>=</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mfrac><mn>1</mn><mi mathvariant="normal">b</mi></mfrac><msqrt><mi>ab</mi><mo> </mo></msqrt><mi>nếu</mi><mo> </mo><mi mathvariant="normal">b</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>1</mn><mi mathvariant="normal">b</mi></mfrac><msqrt><mi>ab</mi><mo> </mo></msqrt><mi>nếu</mi><mo> </mo><mi mathvariant="normal">b</mi><mo> </mo><mo><</mo><mo> </mo><mn>0</mn></mtd></mtr></mtable></mfenced></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>1</mn><mi mathvariant="normal">b</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mfrac><mrow><mi mathvariant="normal">b</mi><mo>+</mo><mn>1</mn></mrow><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>1</mn><mfenced open="|" close="|"><mi mathvariant="normal">b</mi></mfenced></mfrac><msqrt><mi mathvariant="normal">b</mi><mo>+</mo><mn>1</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mfrac><mn>1</mn><mi mathvariant="normal">b</mi></mfrac><msqrt><mi mathvariant="normal">b</mi><mo>+</mo><mn>1</mn><mo> </mo></msqrt><mi>nếu</mi><mo> </mo><mi mathvariant="normal">b</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>1</mn><mi mathvariant="normal">b</mi></mfrac><msqrt><mi mathvariant="normal">b</mi><mo>+</mo><mn>1</mn><mo> </mo></msqrt><mi>nếu</mi><mo> </mo><mi mathvariant="normal">b</mi><mo> </mo><mo><</mo><mo> </mo><mn>0</mn></mtd></mtr></mtable></mfenced></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>9</mn><msup><mi mathvariant="normal">a</mi><mn>3</mn></msup></mrow><mrow><mn>36</mn><mi mathvariant="normal">b</mi></mrow></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mfrac><mrow><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo>.</mo><mi mathvariant="normal">a</mi><mo>.</mo><mi mathvariant="normal">b</mi></mrow><mrow><mi>ab</mi><mo>.</mo><mi mathvariant="normal">b</mi></mrow></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced open="|" close="|"><mfrac><mi mathvariant="normal">a</mi><mrow><mn>2</mn><mi mathvariant="normal">b</mi></mrow></mfrac></mfenced><msqrt><mi>ab</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mfrac><mi mathvariant="normal">a</mi><mrow><mn>2</mn><mi mathvariant="normal">b</mi></mrow></mfrac><msqrt><mi>ab</mi><mo> </mo></msqrt><mi>nếu</mi><mo> </mo><mi mathvariant="normal">a</mi><mo>.</mo><mi mathvariant="normal">b</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mi mathvariant="normal">a</mi><mrow><mn>2</mn><mi mathvariant="normal">b</mi></mrow></mfrac><msqrt><mi>ab</mi></msqrt><mo> </mo><mi>nếu</mi><mo> </mo><mi mathvariant="normal">a</mi><mo>.</mo><mi mathvariant="normal">b</mi><mo> </mo><mo><</mo><mo> </mo><mn>0</mn></mtd></mtr></mtable></mfenced></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi>xy</mi><msqrt><mfrac><mn>2</mn><mi>xy</mi></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><msqrt><mfrac><mrow><mn>2</mn><msup><mrow><mo>(</mo><mi>xy</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow><mi>xy</mi></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><msqrt><mn>2</mn><mi>xy</mi></msqrt><mo> </mo><mo mathvariant="italic">(</mo><mi>d</mi><mi>o</mi><mo mathvariant="italic"> </mo><mi>x</mi><mi>y</mi><mo mathvariant="italic"> </mo><mo mathvariant="italic">></mo><mo mathvariant="italic"> </mo><mn mathvariant="italic">0</mn><mo mathvariant="italic"> </mo><mi>n</mi><mi>ê</mi><mi>n</mi><mo mathvariant="italic"> </mo><mi>d</mi><mi>ư</mi><mo mathvariant="italic"> </mo><mi>t</mi><mi>h</mi><mi>ừ</mi><mi>a</mi><mo mathvariant="italic"> </mo><mi>s</mi><mi>ố</mi><mo mathvariant="italic"> </mo><mi>x</mi><mi>y</mi><mo mathvariant="italic"> </mo><mi>v</mi><mi>à</mi><mi>o</mi><mo mathvariant="italic"> </mo><mi>t</mi><mi>r</mi><mi>o</mi><mi>n</mi><mi>g</mi><mo mathvariant="italic"> </mo><mi>d</mi><mi>ấ</mi><mi>u</mi><mo mathvariant="italic"> </mo><mi>c</mi><mi>ă</mi><mi>n</mi><mo mathvariant="italic">)</mo></math>