Let-a-b-c-0-and-a-2-b-2-c-2-3-Prove-that-a-3-b-c-3-9-

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 .