Hướng dẫn Giải Bài 60 (trang 33, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 60 (Trang 33 SGK Toán 9, Tập 1)

Bài 60 (Trang 33 SGK Toán 9, Tập 1): Cho biểu thức <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>16</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>16</mn></msqrt><mo> </mo><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>9</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>9</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>4</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>4</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></msqrt><mo> </mo><mi>với</mi><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>≥</mo><mo> </mo><mn>1</mn></math> a) Rút gọn biểu thức B. b) Tìm x sao cho B có giá trị là 16.   Hướng dẫn giải: a)  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>16</mn><mo>(</mo><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>9</mn><mo>(</mo><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>4</mn><mo>(</mo><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></msqrt><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn><msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>3</mn><msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></msqrt><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></msqrt><mo>(</mo><mn>4</mn><mo> </mo><mo>-</mo><mo> </mo><mn>3</mn><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn><msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></msqrt></math> b) B = 16 nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>16</mn><mo> </mo><mo>⇔</mo><mo> </mo><msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn><mo> </mo><mo>⇔</mo><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mn>16</mn><mo> </mo><mo>⇔</mo><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>15</mn><mo>.</mo></math>