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 : $[(a+b)^3-3ab(a+b)]^2$

Multiplying out and cancelling leaves $$a^2b^4+a^4b^2\ge2a^3b^3$$ which let's write as $${a^2b^4+a^4b^2\over2}\ge a^3b^3$$ which is true by the inequality of the arithmetic and geometric means. 
