a, b, c ∈ nonnegative real numbers (√(a^2 + b^2 + 1)) + (√(b^2 + c^2 + 1)) + (√(c^2 + a^2 + 1)) ≥ 2 + (√(2(a^2 + b^2 + c^2 ) + 1)) Find all triplets (a, b, c) so that inequality above hold .


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Question Number 69229 by naka3546 last updated on 21/Sep/19

$a, b, c \in n o n n e g a t i v e r e a l n u m b e r s$ $\sqrt{a^{2} + b^{2} + 1} + \sqrt{b^{2} + c^{2} + 1} + \sqrt{c^{2} + a^{2} + 1} ⩾ 2 + \sqrt{2 (a^{2} + b^{2} + c^{2}) + 1}$ $F i n d a l l t r i p l e t s (a, b, c) s o t h a t i n e q u a l i t y a b o v e h o l d .$
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