A two variable Inequality Show that $(a^2+b^2)(a^4+b^4) \geq (a^3+b^3)^2$ 
Can we go like this : $(a^2+b^2)=(a+b)^2-2ab \& (a^4+b^4) = (a^2+b^2)^2-2a^2b^2$  and right hand side of the inequality : $[(a+b)^3-3ab(a+b)]^2$

Are there any restrictions on $a,b$? RHS is $a^3+b^3 = (a+b)(a^2+b^2-ab)$. Clearly for all $|a|,|b|>1 \ \ a^2+b^2 >a^2+b^2 -ab$ and $ a^4+ b^4> a+b$
