用函数方法证明不等式 ,常常能够方便地给出证明 .用函数方法证明不等式的关键是结合不等式的结构特征构造适当的函数 ,以便于利用这一函数的有关性质证明所给的不等式 .例 1　若ａ ｂ0 ,ｍ 0 .求证 :ａｂ ａ +ｍｂ+ｍ.证明　令 ｆ(ｘ) =ａ+ｘｂ +ｘ.由ａｂ可设ａ =ｂ+ｃ( Using functional methods to prove inequalities, it is often convenient to give proofs. The key to using function methods to prove inequalities is to construct appropriate functions in combination with structural features of inequalities so that the inequality given can be proved by using the properties of this function. Example 1 a b0 ,m 0 . Proof: ab a +mb+m. Prove that f(x) =a+xb +x. From ab, set a =b+c(