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Question Number 145240 by loveineq last updated on 03/Jul/21

Let a, b, c ⩾ 0 and a^{2} + b^{2} + c^{2} = 3 . Prove that

(1) \sum_{c y c} a^{3} + \sum_{c y c} {(a + b)}^{3} ⩽ 27

(2) a^{3} + b^{3} + {(b + c)}^{3} + {(c + a)}^{3} ⩾ \frac{1}{2} [c^{3} + {(a + b)}^{3}]

(3) For a ⩾ b ⩾ c ⩾ 0,

a^{3} + b^{3} + {(b + c)}^{3} + {(c + a)}^{3} ⩽ 2 [c^{3} + {(a + b)}^{3}]

Answered by mitica last updated on 03/Jul/21

Commented by loveineq last updated on 03/Jul/21

t h a n k s y o u . I f i n d y o u!!!!!