Hướng dẫn Giải Bài 73 (trang 40, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 73 (Trang 40 SGK Toán 9, Tập 1)

Bài 73 (Trang 40 SGK Toán 9, Tập 1): Rút gọn giá trị của các biểu thức sau: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><msqrt><mn>9</mn><mi mathvariant="normal">a</mi></msqrt><mo>-</mo><msqrt><mn>9</mn><mo>+</mo><mn>12</mn><mi mathvariant="normal">a</mi><mo>+</mo><mn>4</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup></msqrt><mo> </mo><mi>tại</mi><mo> </mo><mi mathvariant="normal">a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>9</mn><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">m</mi></mrow><mrow><mi mathvariant="normal">m</mi><mo>-</mo><mn>2</mn></mrow></mfrac><msqrt><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mi mathvariant="normal">m</mi><mo>+</mo><mn>4</mn></msqrt><mo> </mo><mi>tại</mi><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>;</mo></math> c)<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>)</mo><mo> </mo><msqrt><mn>1</mn><mo>-</mo><mn>10</mn><mi mathvariant="normal">a</mi><mo>+</mo><mn>25</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup></msqrt><mo>-</mo><mn>4</mn><mi mathvariant="normal">a</mi><mo> </mo><mi>tại</mi><mo> </mo><mi mathvariant="normal">a</mi><mo>=</mo><mo> </mo><msqrt><mn>2</mn></msqrt><mo>;</mo></math> 4x- <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mn>4</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>9</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>1</mn></msqrt><mo> </mo><mi>tại</mi><mo> </mo><mi mathvariant="normal">x</mi><mo>=</mo><mo>-</mo><msqrt><mn>3</mn></msqrt><mo>.</mo></math>   Hướng dẫn giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><msqrt><mn>9</mn><mi mathvariant="normal">a</mi></msqrt><mo>-</mo><msqrt><mn>9</mn><mo>+</mo><mn>12</mn><mi mathvariant="normal">a</mi><mo>+</mo><mn>4</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><msup><mn>3</mn><mn>2</mn></msup><mo>.</mo><mfenced><mrow><mo>-</mo><mi>a</mi></mrow></mfenced></msqrt><mo>-</mo><msqrt><msup><mn>3</mn><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>.</mo><mn>2</mn><mi>a</mi><mo>+</mo><msup><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><msqrt><mo>-</mo><mi>a</mi></msqrt><mo>-</mo><msqrt><msup><mfenced><mrow><mn>3</mn><mo>+</mo><mn>2</mn><mi>a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><msqrt><mo>-</mo><mi>a</mi><mo> </mo></msqrt><mo>-</mo><mfenced open="|" close="|"><mrow><mn>3</mn><mo>+</mo><mn>2</mn><mi>a</mi></mrow></mfenced></math> Tại a = 9 ta được: 3<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><msqrt><mo>-</mo><mfenced><mrow><mo>-</mo><mn>9</mn></mrow></mfenced></msqrt><mo>-</mo><mfenced open="|" close="|"><mrow><mn>3</mn><mo>+</mo><mn>2</mn><mfenced><mrow><mo>-</mo><mn>9</mn></mrow></mfenced></mrow></mfenced><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><msqrt><msup><mn>3</mn><mn>2</mn></msup></msqrt><mo> </mo><mo>-</mo><mfenced open="|" close="|"><mrow><mn>3</mn><mo>-</mo><mn>18</mn></mrow></mfenced><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mo>.</mo><mn>3</mn><mo> </mo><mo>-</mo><mo> </mo><mfenced open="|" close="|"><mrow><mo>-</mo><mn>15</mn></mrow></mfenced><mo> </mo><mo>=</mo><mo> </mo><mn>9</mn><mo> </mo><mo>-</mo><mo> </mo><mn>15</mn><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>6</mn></math>. b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">m</mi></mrow><mrow><mi mathvariant="normal">m</mi><mo>-</mo><mn>2</mn></mrow></mfrac><msqrt><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mi mathvariant="normal">m</mi><mo>+</mo><mn>4</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">m</mi></mrow><mrow><mi mathvariant="normal">m</mi><mo>-</mo><mn>2</mn></mrow></mfrac><msqrt><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>.</mo><mn>2</mn><mi mathvariant="normal">m</mi><mo>+</mo><msup><mn>2</mn><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">m</mi></mrow><mrow><mi mathvariant="normal">m</mi><mo>-</mo><mn>2</mn></mrow></mfrac><msqrt><msup><mfenced><mrow><mi mathvariant="normal">m</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">m</mi></mrow><mrow><mi mathvariant="normal">m</mi><mo>-</mo><mn>2</mn></mrow></mfrac><mfenced open="|" close="|"><mrow><mi mathvariant="normal">m</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math>                   Tại m = 1,5 ta được: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><mfrac><mrow><mn>3</mn><mo>.</mo><mn>1</mn><mo>,</mo><mn>5</mn></mrow><mrow><mn>1</mn><mo>,</mo><mn>5</mn><mo> </mo><mo>-</mo><mn>2</mn></mrow></mfrac><mfenced open="|" close="|"><mrow><mn>1</mn><mo>,</mo><mn>5</mn><mo>-</mo><mn>2</mn></mrow></mfenced><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><mfrac><mrow><mn>4</mn><mo>,</mo><mn>5</mn></mrow><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfrac><mo>.</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo>-</mo><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mo>=</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>.</mo></math> c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>1</mn><mo>-</mo><mn>10</mn><mi>a</mi><mo>+</mo><mn>25</mn><msup><mi>a</mi><mn>2</mn></msup></msqrt><mo> </mo><mo>-</mo><mn>4</mn><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>1</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn><mi>a</mi><mo>+</mo><msup><mfenced><mrow><mn>5</mn><mi>a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo> </mo><mo>-</mo><mn>4</mn><mi>a</mi><mo>=</mo><mo> </mo><msqrt><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>5</mn><mi>a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo>-</mo><mn>4</mn><mi>a</mi><mo> </mo><mo>=</mo><mfenced open="|" close="|"><mrow><mn>1</mn><mo>-</mo><mn>5</mn><mi>a</mi></mrow></mfenced><mo>-</mo><mn>4</mn><mi>a</mi></math> Tại a = <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math> ta được <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mrow><mn>1</mn><mo>-</mo><mn>5</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced><mo>-</mo><mn>4</mn><msqrt><mn>2</mn><mo> </mo></msqrt><mo>=</mo><mfenced><mrow><mn>1</mn><mo>-</mo><mn>5</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced><mo>-</mo><mn>4</mn><msqrt><mn>2</mn><mo> </mo></msqrt><mo>=</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>1</mn></math> d) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi>x</mi><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><mn>4</mn><mi>x</mi><mo>-</mo><msqrt><msup><mfenced><mrow><mn>3</mn><mi>x</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>.</mo><mn>3</mn><mi>x</mi><mo>+</mo><msup><mn>1</mn><mn>2</mn></msup></msqrt><mo>=</mo><mn>4</mn><mi>x</mi><mo> </mo><mo>-</mo><msqrt><msup><mfenced><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mn>4</mn><mi>x</mi><mo>-</mo><mfenced open="|" close="|"><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math> Tại <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><msqrt><mn>3</mn></msqrt><mo> </mo><mi>ta</mi><mo> </mo><mi>được</mi><mo>:</mo><mo> </mo><mn>4</mn><mfenced><mrow><mo>-</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mo> </mo><mo>-</mo><mo> </mo><mfenced open="|" close="|"><mrow><mn>3</mn><mfenced><mrow><mo>-</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></mrow></mfenced><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>4</mn><msqrt><mn>3</mn></msqrt><mo> </mo><mo>-</mo><mo> </mo><mfenced open="|" close="|"><mrow><mo>-</mo><mn>3</mn><msqrt><mn>3</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></mrow></mfenced><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>4</mn><msqrt><mn>3</mn></msqrt><mo> </mo><mo>-</mo><mo> </mo><mo>(</mo><mn>3</mn><msqrt><mn>3</mn></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>7</mn><msqrt><mn>3</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></math>