简解一道保送生考试试题的思维历程

• 作 者: 杨春波
• 机 构: 郑州外国语学校,
• 出 处: 数学通讯
• 发表日期: 2015年Z1期
• 关键词: 上海交通大学 平方差公式 一本 分子分母 当且仅当 完全平方

2001年上海交通大学保送生考试数学试题第20题如下:设对于x>0,f(x)=(x+1/x)6-(x6+1/x6)-2/(x+1/x)3+x3+1/x3,求f(x)的最小值.此题结构简单,特征鲜明,一般会被认为是考察运算能力的题目,因为其中涉及到了多项式的6次方、3次方等.直接展开硬算可以解决,但笔者揣测这应该不是命题人的初衷.最终要求f(x)的最小值,但其表达式却是复杂的,则化简工作势在必

Shanghai Jiao Tong University in 2001 to send students to take the exam questions 20 questions as follows: Let x> 0, f (x) = (x +1 / x) 6- (x6 +1 / x6) -2 / (x +1 / x) 3 + x3 + 1 / x3, find the minimum value of f (x) .This question is simple in structure and distinctive in character, and it is generally considered to be the subject of computational abilities because it involves the 6th power of the polynomial and 3 times Square, etc. Directly start hard calculation can be solved, but the author speculated that this should not be the original intention of the proposition. Ultimately require the minimum f (x), but its expression is complicated, the reduction is inevitable