x、y、z属于正实数,且xyz=1,求1/(x^2(y+1)+1)+1/(y^2(z+1)+1)+1/(z^2(x+1)+1)x、y、z属于正实数，且xyz=1，求证1/[x^2(y+1)+1]+1/[y^2(z+1)+1]+1/[z^2(x+1)+1]>=1这是一道证明题，要证明该代数式大于等于1。

Question

x、y、z属于正实数,且xyz=1,求1/(x^2(y+1)+1)+1/(y^2(z+1)+1)+1/(z^2(x+1)+1)
x、y、z属于正实数，且xyz=1，求证1/[x^2(y+1)+1]+1/[y^2(z+1)+1]+1/[z^2(x+1)+1]>=1
这是一道证明题，要证明该代数式大于等于1。

Answer 1

简单方法:
可令X=Y=Z=1
则1/(x^2(y+1)+1)+1/(y^2(z+1)+1)+1/(z^2(x+1)+1)
=1