本文由常见的不等式(a+1a)(b+1b)≥254(a,b∈R+,a+b=1)的证明谈起,运用联想与类比等思维方法,得出几个不等式,用以说明培养学生思维能力的一个方面及推广命题常用的方法.命题1若a,b∈R+且a+b=1,则(a+1a)(b+1b)≥254,当且仅当a=b=12时取“=”号.此命题的证法较多,下面仅用基本不等式和函数的单调性证明.证明∵a,b∈R+,1=a+b≥2槡ab, In this paper, we discuss the common inequalities (a + 1a) (b + 1b) ≥254 (a, b∈R +, a + b = 1) and use some thinking methods such as association and analogy (A + 1a) (b + 1b) ≥254, if and only if a, b∈R + and a + b = 1, and if a = b = 12, then take “= ” number. The proposition of the law more, the following only with basic inequalities and monotonicity of function proof. Prove ∵a, b∈R +, 1 = a + b ≥ 2 槡 ab ,