求证明 x²y²≤(x²+y²)/4

求证明 x²y²≤(x²+y²)/4
求证明 x²y²≤(x²+y²)/4

求证明 x²y²≤(x²+y²)/4
如果有x>0,y>0,则
(x-y)²≥0
↔x²+y²≥2xy
↔x²+2xy+y²≥4xy
↔xy≤(x+y)²/4.
将x换成x²、y换成y²,得
∴x²y²≤(x²+y²)²/4.

x²y²≤(x²+y²)/4
这是有问题
x=y=1
x²y²=1
(x²+y²)/4 = 1/2