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Question

If a,b and c represent the lengths of sides of a triangle, then the possible integral value of ab+c+bc+a+ca+b is

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Solution

We know, 0<a<b+cab+c<1(Triangle Inequality)
ab+c+bc+a+ca+b<3
In the case of a=b=c, we have ab+c=12
32ab+c+bc+a+ca+b<3
Integral values of ab+c+bc+a+ca+b=2

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