Hướng dẫn Giải Bài 31 (trang 19, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 31 (Trang 19 SGK Toán 9, Tập 1)

Bài 31 (Trang 19 SGK Toán 9, Tập 1): a) So sánh <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>25</mn><mo>-</mo><mn>16</mn></msqrt><mo> </mo><mi>và</mi><mo> </mo><msqrt><mn>25</mn></msqrt><mo>-</mo><msqrt><mn>16</mn></msqrt></math> b) Chứng minh rằng, với a > b > 0 thì <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>a</mi></msqrt><mo>-</mo><msqrt><mi>b</mi></msqrt><mo><</mo><msqrt><mi>a</mi><mo>-</mo><mi>b</mi></msqrt></math>   Hướng dẫn giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><msqrt><mn>25</mn><mo>-</mo><mn>16</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>9</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><msup><mn>3</mn><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>25</mn></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>16</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><msup><mn>5</mn><mn>2</mn></msup></msqrt><mo> </mo><mo>-</mo><msqrt><msup><mn>4</mn><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>5</mn><mo> </mo><mo>-</mo><mo> </mo><mn>4</mn><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn></math> Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>25</mn><mo>-</mo><mn>16</mn></msqrt><mo> </mo><mo>></mo><mo> </mo><msqrt><mn>25</mn></msqrt><mo> </mo><mo>-</mo><msqrt><mn>16</mn></msqrt></math> b) Với a > b > 0 để chứng minh <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>a</mi></msqrt><mo>-</mo><msqrt><mi>b</mi></msqrt><mo> </mo><mo><</mo><mo> </mo><msqrt><mi>a</mi><mo>-</mo><mi>b</mi></msqrt></math> ta quy về so sánh <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>a</mi></msqrt><mo> </mo><mi>v</mi><mi>ớ</mi><mi>i</mi><mo> </mo><msqrt><mi>a</mi><mo>-</mo><mi>b</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>b</mi></msqrt></math> Áp dụng kết quả bài 26 với hai số (a - b) và b ta sẽ được:  <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>a</mi><mo>-</mo><mi>b</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>b</mi></msqrt><mo> </mo><mo>></mo><mo> </mo><msqrt><mi>a</mi><mo>-</mo><mi>b</mi><mo>+</mo><mi>b</mi></msqrt><mo> </mo><mi>h</mi><mi>a</mi><mi>y</mi><mo> </mo><msqrt><mi>a</mi><mo>-</mo><mi>b</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>b</mi></msqrt><mo> </mo><mo>></mo><mo> </mo><msqrt><mi>a</mi></msqrt><mo>.</mo></math> Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>a</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi>b</mi><mo> </mo></msqrt><mo> </mo><mo><</mo><mo> </mo><msqrt><mi>a</mi><mo>-</mo><mi>b</mi></msqrt></math>