An algebra problem by Ankit Sharma
Let a , b , and c be positive real numbers such that {a^2}/{2018-a}+{b^2}/{2018-b}+{c^2}/{2018-c}={1}/{168}. What is the largest possible value of a+b+c ?
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1 solution
Obviously the symmetry begs us to have a=b=c . Try a=2 . It works. Then a+b+c = 6
Or you could waste time with Cauchy-Engel...