prove-a-2-b-2-c-2-abc-1-3-4-if-ab-bc-ac-3-

Question Number 204948 by TonyCWX08 last updated on 03/Mar/24

p r o v e

a^{2} + b^{2} + c^{2} + \sqrt[3]{a b c} ⩾ 4

i f

a b + b c + a c = 3

Commented by TonyCWX08 last updated on 04/Mar/24

C a n a n y o n e p l e a s e h e l p ? ? ?

Commented by mr W last updated on 04/Mar/24

q u e s t i o n i s w r o n g!

w i t h a = b = c = - 1 y o u h a v e

a b + b c + c a = 3

b u t a^{2} + b^{2} + c^{2} + \sqrt[3]{a b c} = 1 + 1 + 1 - 1 = 2 ⩾ 4

Commented by mr W last updated on 04/Mar/24

m a y b e y o u s h o u l d s t a t e a, b, c \in R^{+}

Commented by TonyCWX08 last updated on 05/Mar/24

T h e y A r e P o s i t i v e R e a l N u m b e r s \dots . .