证明x^2+1/(x^2+1)>1(x不等于0)用基本不等式证

题目

证明x^2+1/(x^2+1)>1(x不等于0)用基本不等式证

答案

x^2+1>0
(x^2+1)+1/(x^2+1)
>=2√[(x^2+1)*1/(x^2+1)]=2
x≠0,x^2+1≠1/(x^2+1)
=号不成立
即x^2+1+1/(x^2+1)>2
所以
x^2+1/(x^2+1)>1