Prove-that-a-2-b-2-c-2-6-3-a-b-c-a-b-c-R-

Question Number 126175 by naka3546 last updated on 17/Dec/20

P r o v e t h a t

a^{2} + b^{2} + c^{2} + 6 ⩾ 3 (a + b + c)

a, b, c \in R^{+}

Commented by PRITHWISH SEN 2 last updated on 18/Dec/20

{(a - 2)}^{2} ⩾ - (a - 2) equality holds for a = 1

\Rightarrow a^{2} + 2 ⩾ 3 a

similariy

b^{2} + 2 ⩾ 3 b

c^{2} + 2 ⩾ 3 c

adding

a^{2} + b^{2} + c^{2} + 6 ⩾ 3 (a + b + c)