《中学数学教学参考》2 0 0 2年第 8斯 ｐ .2 7上有这样两个不等式 :若ａ ,ｂ∈Ｒ+ ,ａ+ｂ =1,则43 ≤ 1ａ+1+1ｂ+132 ,32 1ａ2 +1+1ｂ2 +1≤ 85 .经过类比、猜测、证明 ,笔者得到两个新的结果 ,兹介绍如下 .定理 1　若ａ ,ｂ∈Ｒ+ ,ａ +ｂ=1,则32 1ａ3 +1+1ｂ3 +1≤ 169.证 There are two inequalities on the 8th p.2 7 of the “Middle School Mathematics Teaching Reference” in 2002: if a, b∈R+, a+b =1, 43 ≤ 1a+1+1b+132, 32 1a2 +1+1b2 +1≤ 85. After analogy, guessing, and proof, the author gets two new results, which are described below. Theorem 1 If a, b∈R+, a +b=1, then 32 1a3 + 1+1b3 +1≤169.