Question

For all `a,b,c >=1 ` that satisfy `a+b+c= 2abc `

Prove that `root (3) ((a+b+c)^2) >= sum_{cyc} root (3) (ab-1) `

Difficulty level (1 very easy - 10 very hard): 6

Topics:
Algebra -> Inequalities -> Averages / Means
Sources:
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