Hướng dẫn Giải Bài 52 (trang 30, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 52 (Trang 30 SGK Toán 9, Tập 1)

Bài 52 (Trang 30 SGK Toán 9, Tập 1): Trục căn thức ở mẫu với giả thiết các biểu thức chữ đều có nghĩa <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mrow><msqrt><mn>6</mn></msqrt><mo>-</mo><msqrt><mn>5</mn></msqrt></mrow></mfrac><mo>;</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfrac><mn>3</mn><mrow><msqrt><mn>10</mn></msqrt><mo>+</mo><msqrt><mn>7</mn></msqrt></mrow></mfrac><mo>;</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfrac><mn>1</mn><mrow><msqrt><mi mathvariant="normal">x</mi></msqrt><mo>-</mo><msqrt><mi mathvariant="normal">y</mi></msqrt></mrow></mfrac><mo>;</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfrac><mrow><mn>2</mn><mi>ab</mi></mrow><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>-</mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfrac><mo>.</mo></math>   Hướng dẫn giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mrow><msqrt><mn>6</mn></msqrt><mo>-</mo><msqrt><mn>5</mn></msqrt></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>2</mn><mo>(</mo><msqrt><mn>6</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt><mo>)</mo></mrow><mrow><mo>(</mo><msqrt><mn>6</mn></msqrt><mo>-</mo><msqrt><mn>5</mn></msqrt><mo>)</mo><mo>(</mo><msqrt><mn>6</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt><mo>)</mo></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>2</mn><mo>(</mo><msqrt><mn>6</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt><mo>)</mo></mrow><mrow><mn>6</mn><mo>-</mo><mn>5</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mo>(</mo><msqrt><mn>6</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt><mo>)</mo><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mrow><msqrt><mn>10</mn></msqrt><mo>+</mo><msqrt><mn>7</mn></msqrt></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>3</mn><mo>(</mo><msqrt><mn>10</mn></msqrt><mo>-</mo><msqrt><mn>7</mn></msqrt><mo>)</mo></mrow><mrow><mo>(</mo><msqrt><mn>10</mn></msqrt><mo>+</mo><msqrt><mn>7</mn></msqrt><mo>)</mo><mo>(</mo><msqrt><mn>10</mn></msqrt><mo>-</mo><msqrt><mn>7</mn></msqrt><mo>)</mo></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>3</mn><mo>(</mo><msqrt><mn>10</mn></msqrt><mo>-</mo><msqrt><mn>7</mn></msqrt><mo>)</mo></mrow><mrow><mn>10</mn><mo>-</mo><mn>7</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>10</mn></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>7</mn></msqrt><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><msqrt><mi mathvariant="normal">x</mi></msqrt><mo>-</mo><msqrt><mi mathvariant="normal">y</mi></msqrt></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>1</mn><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo></mrow><mrow><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo>-</mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt></mrow><mrow><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">y</mi></mrow></mfrac><mo> </mo><mo mathvariant="italic">(</mo><mi>d</mi><mi>o</mi><mo mathvariant="italic"> </mo><mi>x</mi><mo mathvariant="italic"> </mo><mo mathvariant="italic">≠</mo><mo mathvariant="italic"> </mo><mi>y</mi><mo mathvariant="italic"> </mo><mi>n</mi><mi>ê</mi><mi>n</mi><mo mathvariant="italic"> </mo><msqrt><mi mathvariant="italic">x</mi></msqrt><mo mathvariant="italic"> </mo><mo mathvariant="italic">≠</mo><mo mathvariant="italic"> </mo><msqrt><mi mathvariant="italic">y</mi></msqrt><mo mathvariant="italic">)</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>ab</mi></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><mn>2</mn><mi>ab</mi><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><mn>2</mn><mi>ab</mi><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo></mrow><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfrac><mo> </mo><mo mathvariant="italic">(</mo><mi>d</mi><mi>o</mi><mo mathvariant="italic"> </mo><mi>a</mi><mo mathvariant="italic"> </mo><mo mathvariant="italic">≠</mo><mo mathvariant="italic"> </mo><mi>b</mi><mo mathvariant="italic"> </mo><mi>n</mi><mi>ê</mi><mi>n</mi><mo mathvariant="italic"> </mo><msqrt><mi mathvariant="italic">a</mi></msqrt><mo mathvariant="italic"> </mo><mo mathvariant="italic">≠</mo><mo mathvariant="italic"> </mo><msqrt><mi mathvariant="italic">b</mi></msqrt><mo mathvariant="italic">)</mo></math>