文 [1 ]、[2 ]分别用代数、几何法证明了如下无理不等式 :问题 1　若a ,b是正数 ,并且a +b =1 ,则a2 +1 +b2 +1≥ 5 .①我们需要思考的问题是 :不等式①的上界为何 ?经探究 ,得出 :问题 2　若a ,b是正数 ,并且a +b =1 ,则a2 +1 +b2 +1 1 +2 .②证明 :∵ab≤ a +b22 =14 ab∈ 0 The paper [1] and [2] respectively prove the following irrational inequality with algebraic and geometric methods: Problem 1 If a, b are positive, and a +b =1, then a2 +1 +b2 +1 ≥ 5 .1 we need The question of thinking is: What is the upper bound of inequality 1? After investigation, we have found: Question 2 If a, b is positive and a +b = 1, then a2 +1 +b2 +1 1 +2 .2 proves: Ab≤ a +b22 =14 ab∈ 0