设函数f(x)=|2-x^2|,若0＜m＜n,且f（m)=f(n),则mn范围是
问题描述：
设函数f(x)=|2-x^2|,若0＜m＜n,且f（m)=f(n),则mn范围是
答
f(m)^2-f(n)^2=0
(2-m^2)^2-(2-n^20^2=0
m^4-4*m^2-n^4+4*n^2=0
(m^2+n^2)*(m^2-n^2)-4*(m^2-n^2)=0
(m^2+n^2-4)*(m+n)(m-n)=0
因为0
(m-n)^2=m^2-2mn+n^2>0
4-2mn>0
mn因m>0,n>0
故0