Proof that (a^2)/(b) + (b^2)/(c) + (c^2)/(a) >= a+b+c

Damon Vazquez 2022-10-09 Answered
Proof that a 2 b + b 2 c + c 2 a a + b + c
I've tried getting everything on the left side and transforming it into something squared so that I can prove it's bigger or equals to 0 but I've been unsuccessful.
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Answers (1)

Cullen Kelly
Answered 2022-10-10 Author has 7 answers
For positives a, b and c by C-S we obtain:
c y c a 2 b ( c y c a ) 2 c y c b = ( a + b + c ) 2 a + b + c = a + b + c .
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