对于某些不等式的证明,若认真分析题目的条件和结论,构造适当的向量,然后借助向量的数量积的性质｜m·n｜≤｜m｜·｜n｜,往往可以使不等式得到证明.一、构造平面向量【例1】已知a,b∈R,求证:(a+b2)2≤a2+b22证明:构造向量m=(a,b),n=(1,1)由｜m·n｜2≤｜m｜2·｜n｜2,得(a+b)2 For the proof of some inequalities, if we carefully analyze the conditions and conclusions of the topic, construct appropriate vectors, and then use the properties of the product of the vectors |m·n|≤|m|·|n|, we can often prove the inequality. First, the construction of the plane vector [Example 1] known a, b ∈ R, verification: (a + b2) 2 ≤ a2 + b22 prove: construct a vector m = (a, b), n = (1, 1) by | m·n|2≤|m|2·|n|2, get (a+b)2