设x,y属于R,证明不等式:(x^2 y^2)^2≥xy(x y)^2

(x²+y²)²-xy(x+y)²
=x^4+2x²y²+y^4-x³y-2x²y²-xy³
=x³(x-y)-y³(x-y)
=(x-y)(x³-y³)
=(x-y)²(x²+xy+y²)
=(x-y)²[(x+y/2)²+3y²/4]>=0
所以(x²+y²)²>=xy(x+y)²