Hướng dẫn giải Bài 5 (Trang 56 SGK Toán Giải Tích 12)

Bài 5 (Trang 56 SGK Toán Giải Tích 12): Chứng minh rằng: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mfrac><mn>1</mn><mn>3</mn></mfrac></mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></msup><mo> </mo><mo><</mo><mo> </mo><msup><mfenced><mfrac><mn>1</mn><mn>3</mn></mfrac></mfenced><mrow><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></msup></math>; b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>7</mn><mrow><mn>6</mn><msqrt><mn>3</mn></msqrt></mrow></msup><mo> </mo><mo>></mo><mo> </mo><msup><mn>7</mn><mrow><mn>3</mn><msqrt><mn>6</mn></msqrt></mrow></msup></math>. Hướng dẫn giải: a) Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msqrt><mn>5</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>20</mn></msqrt><mo>;</mo><mo> </mo><mn>3</mn><msqrt><mn>2</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>18</mn></msqrt></math>. Do vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msqrt><mn>5</mn></msqrt><mo> </mo><mo>></mo><mo> </mo><mn>3</mn><msqrt><mn>2</mn></msqrt></math> Vì <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo><</mo><mn>1</mn><mo> </mo><mi>nên</mi><mo> </mo><msup><mfenced><mfrac><mn>1</mn><mn>3</mn></mfrac></mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></msup><mo><</mo><msup><mfenced><mfrac><mn>1</mn><mn>3</mn></mfrac></mfenced><mrow><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></msup></math> b) Vì <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><msqrt><mn>3</mn></msqrt><mo>=</mo><msqrt><mn>108</mn></msqrt><mo> </mo><mo>></mo><mo> </mo><msqrt><mn>54</mn></msqrt><mo>=</mo><mn>3</mn><msqrt><mn>6</mn></msqrt></math> và 7 > 1 nên <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>7</mn><mrow><mn>6</mn><msqrt><mn>3</mn></msqrt></mrow></msup><mo> </mo><mo>></mo><mo> </mo><msup><mn>7</mn><mrow><mn>3</mn><msqrt><mn>6</mn></msqrt></mrow></msup></math>