Hướng dẫn Giải Bài 61 (trang 33, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 61 (Trang 33 SGK Toán 9, Tập 1)

Bài 61 (Trang 33 SGK Toán 9, Tập 1): Chứng minh các đẳng thức sau: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><mfrac><mn>3</mn><mn>2</mn></mfrac><msqrt><mn>6</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><msqrt><mfrac><mn>2</mn><mn>3</mn></mfrac></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>4</mn><msqrt><mfrac><mn>3</mn><mn>2</mn></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><msqrt><mn>6</mn></msqrt><mn>6</mn></mfrac><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><mo> </mo><mfenced><mrow><mi mathvariant="normal">x</mi><msqrt><mfrac><mn>6</mn><mi mathvariant="normal">x</mi></mfrac></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mfrac><mrow><mn>2</mn><mi mathvariant="normal">x</mi></mrow><mn>3</mn></mfrac></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt></mrow></mfenced><mo> </mo><mo>:</mo><mo> </mo><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mfrac><mn>1</mn><mn>3</mn></mfrac><mo> </mo><mi>với</mi><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn><mo>.</mo></math>   Hướng dẫn giải: a) Thực hiện vế trái: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac><msqrt><mn>6</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><msqrt><mfrac><mn>2</mn><mn>3</mn></mfrac></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>4</mn><msqrt><mfrac><mn>3</mn><mn>2</mn></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>3</mn><mn>2</mn></mfrac><msqrt><mn>6</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>.</mo><msqrt><msup><mn>3</mn><mn>2</mn></msup><mo>.</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><msqrt><msup><mn>2</mn><mn>2</mn></msup><mo>.</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></msqrt><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>3</mn><mn>2</mn></mfrac><msqrt><mn>6</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mfrac><mn>2</mn><mn>3</mn></mfrac><msqrt><mn>6</mn></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><msqrt><mn>6</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><mo> </mo><mo>+</mo><mo> </mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn></mrow></mfenced><msqrt><mn>6</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>1</mn><mn>6</mn></mfrac><msqrt><mn>6</mn></msqrt><mo> </mo><mo>=</mo><mfrac><msqrt><mn>6</mn></msqrt><mn>6</mn></mfrac><mo> </mo><mo>=</mo><mo> </mo><mi>VP</mi></math> Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac><msqrt><mn>6</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><msqrt><mfrac><mn>2</mn><mn>3</mn></mfrac></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>4</mn><msqrt><mfrac><mn>3</mn><mn>2</mn></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><msqrt><mn>6</mn></msqrt><mn>6</mn></mfrac><mo>.</mo></math>   b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>VT</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mi mathvariant="normal">x</mi><msqrt><mfrac><mn>6</mn><mi mathvariant="normal">x</mi></mfrac></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mfrac><mrow><mn>2</mn><mi mathvariant="normal">x</mi></mrow><mn>3</mn></mfrac></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt></mrow></mfenced><mo> </mo><mo>:</mo><mo> </mo><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><msqrt><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>.</mo><mfrac><mn>6</mn><mi mathvariant="normal">x</mi></mfrac></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mfrac><mrow><mn>6</mn><mi mathvariant="normal">x</mi></mrow><mn>3</mn></mfrac><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt></msqrt></mrow></mfenced><mo> </mo><mo>:</mo><mo> </mo><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt></mrow></mfenced><mo> </mo><mo>:</mo><mo> </mo><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>7</mn><mn>3</mn></mfrac><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt><mo>:</mo><msqrt><mn>6</mn><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>7</mn><mn>3</mn></mfrac><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mfrac><mn>1</mn><mn>3</mn></mfrac><mo> </mo><mo>=</mo><mo> </mo><mi>VP</mi><mo>,</mo><mo> </mo><mi>với</mi><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn><mo>.</mo></math>