Hướng dẫn giải Bài 5 (Trang 132 SGK Toán Đại số 9, Tập 2)
<p>Chứng minh rằng giá trị của biểu thức sau không phụ thuộc vào biến:</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mi>x</mi></msqrt></mrow><mrow><mi>x</mi><mo>+</mo><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><msqrt><mi>x</mi></msqrt><mo>-</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>.</mo><mfrac><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt><mo>+</mo><mi>x</mi><mo>-</mo><msqrt><mi>x</mi></msqrt><mo>-</mo><mn>1</mn></mrow><msqrt><mi>x</mi></msqrt></mfrac></math></p>
<p><strong>Giải:</strong></p>
<p>ĐK: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mn>1</mn></math></p>
<p>Đặt <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>x</mi></msqrt><mo>=</mo><mi>a</mi></math> thì biểu thức trở thành:</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>2</mn><mo>+</mo><mi>a</mi></mrow><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mn>2</mn></mrow><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>.</mo><mfrac><mrow><msup><mi>a</mi><mn>3</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mi>a</mi><mo>-</mo><mn>1</mn></mrow><mi>a</mi></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mfenced><mrow><mn>2</mn><mo>+</mo><mi>a</mi></mrow></mfenced><mfenced><mrow><mi>a</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mi>a</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><msup><mfenced><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mfenced><mrow><mi>a</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>.</mo><mfrac><mrow><msup><mi>a</mi><mn>2</mn></msup><mfenced><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mi>a</mi></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mn>2</mn><mi>a</mi><mo>-</mo><mn>2</mn><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mi>a</mi><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi><mo>+</mo><mn>2</mn></mrow><mrow><mfenced><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>a</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>.</mo><mfrac><mrow><mfenced><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mi>a</mi></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mn>2</mn><mi>a</mi></mrow><mi>a</mi></mfrac><mo>=</mo><mn>2</mn></math></p>
<p>Vậy biểu thức không phụ thuộc vào biến.</p>
Hướng dẫn Giải Bài 5, Phần Đại số (Trang 132, SGK Toán 9, Tập 2)