How to prove $2a^4+2b^4 \geq c^2(2a^2+2b^2-c^2)$ for $a,b,c>0$?
2026-03-29 21:02:47.1774818167
How to prove $2a^4+2b^4 \geq c^2(2a^2+2b^2-c^2)$ for any positive $a$, $b$ and $c$?
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$$2a^4+2b^4 \geqslant c^2(2a^2+2b^2-c^2) \iff (a^2-b^2)^2+(a^2+b^2-c^2)^2\geqslant 0$$