if-ab-ac-bc-2-calculate-minimum-of-10a-2-10b-2-c-2-

Question Number 207315 by galva2000 last updated on 11/May/24

i f a b + a c + b c = 2

c a l c u l a t e m i n i m u m o f 10 a^{2} + 10 b^{2} + c^{2}

Answered by Berbere last updated on 11/May/24

S = 10 a^{2} + 10 b^{2} + c = 8 a^{2} + \frac{1}{2} c^{2} + 2 (a^{2} + b^{2}) + 8 b^{2} + \frac{1}{2} c^{2}

x^{2} + y^{2} ⩾ 2 x y

S ⩾ 4 a c + 4 a b + 4 b c = 4 (a b + b c + a c) = 8

M i n = 8

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