Show that for all non-negative numbers $a,b$, $$ 1 + a^{2017} + b^{2017} \geq a^{10}b^{7} + a^{7}b^{2000} + a^{2000}b^{10} $$When is equality attained?
Source: Irish MO 2017 paper 2 problem 4
Tags: algebra, inequalities
Show that for all non-negative numbers $a,b$, $$ 1 + a^{2017} + b^{2017} \geq a^{10}b^{7} + a^{7}b^{2000} + a^{2000}b^{10} $$When is equality attained?