Maximum Value

Algebra Level 4

a,b,ca,b,c are non-negative real numbers satisfying a+b+c=1a+b+c=1.

The maximum value of

ab+bc+ca−2abcab+bc+ca-2abc

can be written as mn\frac{m}{n} ; where m,n m,n are relatively prime. Find m+nm+n.

Fahim Shahriar Shakkhor by Fahim Shahriar Shakkhor
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