Let a≥b≥c≥0 and a^2 +b^2 +c^2 = 3. Prove that a^3 +(b+c)^3 ≤ 9


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Question Number 145137 by loveineq last updated on 02/Jul/21

$Let a ⩾ b ⩾ c ⩾ 0 and a^{2} + b^{2} + c^{2} = 3 . Prove that$ $a^{3} + {(b + c)}^{3} ⩽ 9$
Commented by justtry last updated on 02/Jul/21

Commented by puissant last updated on 02/Jul/21

$merci$
Commented by loveineq last updated on 02/Jul/21

$is that proving inequality ?$
	Answered by mitica last updated on 02/Jul/21

	Answered by mitica last updated on 02/Jul/21

	$f (a) = a^{3} + \sqrt{{(6 - 2 a^{2})}^{3}}, f : [1, \sqrt{3}] \to R$ $a = 1 m a x i m u m p o i n t$
	Commented by loveineq last updated on 02/Jul/21

	$Ok, i see . thanks .$
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