parmenides51 wrote: Prove that for all $ x, y \in 0, 1 $ the inequality $ 5 (x^2+ y^2) ^2 \leq 4 + (x +y) ^4$ holds. Prove that for all $ x, y \in [0, 1] $ the inequality $ 5 (x^2+ y^2) ^2 \leq 4 + (x +y) ^4$ holds. $$ 5 (x^2+ y^2) ^2 \leq 4 + (x +y) ^4\iff x^4+ y^4+x^2y^2\le 1+x^3y+ xy^3$$

it is the solution

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bakar wrote: it is the solution

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