题目已知a,b,c,d都是正数,且a~2+b~2=1,c~2+d~2=1.求证:ac+bd≤1.这是一道常见而又典型的题目,题目的证明难度不大,但它蕴含的数学思想及方法却较为丰富.思路分析1根据题目a~2+b~2,c~2+d~2及ac+bd的结构,联想到初中一道典型的因式分解题目:分解 It is known that a, b, c, d are all positive numbers, and a~2+b~2=1, c~2+d~2=1. Proof: ac+bd≤1. This is a common and typical The title of the title, the proof of the title is not difficult, but it contains more mathematical ideas and methods are more abundant. Idea analysis 1 according to the title of a~2+b~2,c~2+d~2 and ac+bd structure, association A typical factorization problem in junior high school: Decomposition