PMO 2021 Problem 7

Let $a, b, c,$ and $d$ be real numbers such that $a \geq b \geq c \geq d$ and $a+b+c+d = 13$ $a^2+b^2+c^2+d^2=43.$ Show that $ab \geq 3 + cd$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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