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Question Number 164926 by Zaynal last updated on 23/Jan/22

⌊ Given positive numbers a, b, c, d ⌉

Prove that;

⌊ \frac{a^{3} + b^{3} + c^{3}}{a + b + c} + \frac{b^{3} + c^{3} + d^{3}}{b + c + d} + \frac{c^{3} + d^{3} + a^{3}}{c + d + a} + \frac{d^{3} + a^{3} + b^{3}}{d + a + b} > a^{2} + b^{2} + c^{2} + d^{2} ⌋