Prove that there are $a, b,$ positive numbers such that:
$f(x,y)=x^4+y^4-2(x-y)^2 \geq a(x^2+y^2)-b$
I've tried using the fact that $x^4 + y^4 \geq 2(xy)^2$ and also that $xy\geq -(1/2)(x^2+y^2)$
I've also tried that:
$f(x,y)\gt 2(xy)^2 -2(x-y)^2 = 2(xy)^2 -2(x^2+y^2) +4xy$
I factorized $xy$ and it didn't work so i don't know if i'm on the right way
I'll appreciate any help or hint.