Question-217690

Question Number 217690 by hardmath last updated on 18/Mar/25

Commented by hardmath last updated on 18/Mar/25

★ Hard ★

Commented by mr W last updated on 19/Mar/25

★ Hard m a t h ★

Commented by hardmath last updated on 19/Mar/25

y es dear professor))

Answered by mr W last updated on 19/Mar/25

s a y A I = x, B I = y, C I = z

x y z = 4 {R r}^{2}

R ⩾ 2 r

x + y + z ⩾ 3 \sqrt[3]{x y z} = 3 \sqrt[3]{4 {R r}^{2}} ⩾ 3 \sqrt[3]{8 r^{3}} = 6 r

\dots

Commented by hardmath last updated on 19/Mar/25

dear professor, {that}^{'} s it ?)

Commented by mr W last updated on 19/Mar/25

{w h a t}^{'} s i t w h a t y o u m e a n ?

Commented by hardmath last updated on 19/Mar/25

That is, the solution (proof) is this value

Commented by mr W last updated on 19/Mar/25

a s y o u c a n s e e, i t i s o n l y t h e p r o o f

f o r t h e p a r t 6 r ⩽ A I + B I + C I

Commented by mr W last updated on 19/Mar/25

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