Inequalities

[Guest]

Hi, can I have some help to solve this inequality? I am having a lot of trouble with it. Thanks.


The problem is:
L.H.S=(x^4)(y^2)+(x^2)(y^4)+x+y
R.H.S.=(x^2)(y)+(x)(y^2)+2(x^2)(y^2)
Prove that L.H.S≥R.H.S, for all positive x and y.