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Question

If a,b,care lengths of the sides of a triangle, then (a+b+c)3 is


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Solution

Finding the value of (a+b+c)3:

Given a,b,c are lengths of sides of a triangle

a+b>cora+bc>0b+c>aorb+ca>0c+a>borc+ab>0[(a+bc)(b+ca)(c+ab)]1/3[AMof3quantitiesGMof3quantities][a+b+c]/3[(a+bc)(b+ca)(c+ab)]1/3(a+b+c)327[(a+bc)(b+ca)(c+ab)]Hence, the value of (a+b+c)327[(a+bc)(b+ca)(c+ab)]


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