calculus-a-b-c-R-find-min-b-c-a-a-c-b-a-b-c-m-n-1970-

Question Number 116798 by mnjuly1970 last updated on 06/Oct/20

\dots c a l c u l u s \dots

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

f i n d

m i n (\sqrt{\frac{b + c}{a}} + \sqrt{\frac{a + c}{b}} + \sqrt{\frac{a + b}{c}}) = ? ? ?

\dots m . n . 1970 \dots

Answered by mr W last updated on 06/Oct/20

⩾ \sqrt{\frac{2 \sqrt{b c}}{a}} + \sqrt{\frac{2 \sqrt{a c}}{b}} + \sqrt{\frac{2 \sqrt{a b}}{c}}

⩾ 3 \sqrt[3]{\sqrt{\frac{8 a b c}{a b c}}} = 3 \sqrt{2}

Commented by mnjuly1970 last updated on 07/Oct/20

t a y y e b a l l a h t h a n k y o u . .