If-a-1-b-1-c-1-8-Then-a-2-b-2-c-2-3-

Question Number 205422 by hardmath last updated on 20/Mar/24

If

(a + 1) (b + 1) (c + 1) = 8

Then :

a^{2} + b^{2} + c^{2} ⩾ 3

Answered by A5T last updated on 20/Mar/24

a + 1 + b + 1 + c + 1 ⩾ 3 \sqrt[3]{(a + 1) (b + 1) (c + 1)} = 6

\Rightarrow a + b + c ⩾ 3

\sqrt{3} \sqrt{a^{2} + b^{2} + c^{2}} ⩾ a + b + c \Rightarrow a^{2} + b^{2} + c^{2} ⩾ 3

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