Question

докажите неравенство a⁴+2a³b+2ab³+b⁴≥6a²b²

Answer 1

a^4-2a^2b^2+b^4+2a^3b-4a^2b^2+2ab^3>0
(a^2-b^2)+2ab(a-b)^2>0
ab>0
(a^2-b^2)+2ab(a-b)^2>0