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anemone
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Let $a,\,b,\,c$ and $d$ be non-negative real numbers such that $a + b + c + d = 2$.
Prove that $ab(a^2+ b^2 + c^2) + bc(b^2+ c^2+ d^2) + cd(c^2+ d^2+ a^2) + da(d^2+ a^2+ b^2) ≤ 2$.
Prove that $ab(a^2+ b^2 + c^2) + bc(b^2+ c^2+ d^2) + cd(c^2+ d^2+ a^2) + da(d^2+ a^2+ b^2) ≤ 2$.