Hướng dẫn Giải Bài 74 (trang 40, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 74 (Trang 40 SGK Toán 9, Tập 1)

Bài 74 (Trang 40 SGK Toán 9, Tập 1): Tìm x biết: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><msqrt><msup><mfenced><mrow><mn>2</mn><mi mathvariant="normal">x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><mfrac><mn>5</mn><mn>3</mn></mfrac><msqrt><mn>15</mn><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>15</mn><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>15</mn><mi mathvariant="normal">x</mi></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><msup><mfenced><mrow><mn>2</mn><mi mathvariant="normal">x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mo> </mo><mo>⇔</mo><mfenced open="|" close="|"><mrow><mn>2</mn><mi mathvariant="normal">x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn></math> -) Nếu <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo> </mo><mo>≥</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo> </mo><mi>thì</mi><mo> </mo><mn>2</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mo> </mo><mo>⇔</mo><mo> </mo><mn>2</mn><mi mathvariant="normal">x</mi><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>2</mn><mo> </mo><mo>(</mo><mi>Thỏa</mi><mo> </mo><mi>mãn</mi><mo>)</mo></math> -) Nếu <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo><</mo><mo> </mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo> </mo><mi>t</mi><mi>h</mi><mi>ì</mi><mo> </mo><mn>2</mn><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mo> </mo><mo>⇔</mo><mo> </mo><mo>-</mo><mn>2</mn><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mo> </mo><mo>⇔</mo><mo> </mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>1</mn><mo>.</mo></math> Vậy phương trình có hai nghiệm x = 2 và x = -1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><mfrac><mn>5</mn><mn>3</mn></mfrac><msqrt><mn>15</mn><mi mathvariant="normal">x</mi><mo> </mo></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>15</mn><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>15</mn><mi mathvariant="normal">x</mi><mo> </mo></msqrt><mo> </mo><mo>(</mo><mi>Đ</mi><mi>i</mi><mi>ề</mi><mi>u</mi><mo> </mo><mi>k</mi><mi>i</mi><mi>ệ</mi><mi>n</mi><mo> </mo><mi>x</mi><mo> </mo><mo>≥</mo><mo> </mo><mn>0</mn><mo>)</mo><mo>.</mo><mspace linebreak="newline"/><mo>⇔</mo><mo> </mo><mfrac><mn>5</mn><mn>3</mn></mfrac><msqrt><mn>15</mn><mi>x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>15</mn><mi>x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>15</mn><mi>x</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mspace linebreak="newline"/><mo>⇔</mo><mo> </mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>15</mn><mi>x</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mspace linebreak="newline"/><mo>⇔</mo><msqrt><mn>15</mn><mi>x</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>6</mn><mspace linebreak="newline"/><mo>⇔</mo><mo> </mo><mn>15</mn><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>36</mn><mspace linebreak="newline"/><mo>⇔</mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>36</mn><mn>15</mn></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>12</mn><mn>5</mn></mfrac><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mfrac><mn>2</mn><mn>5</mn></mfrac><mo>.</mo></math>