If a,b,care lengths of the sides of a triangle, then (a+b+c)3 is
Finding the value of (a+b+c)3:
Given a,b,c are lengths of sides of a triangle
a+b>cora+b–c>0b+c>aorb+c–a>0c+a>borc+a–b>0[(a+b–c)(b+c–a)(c+a–b)]1/3≥[AMof3quantities≥GMof3quantities][a+b+c]/3≥[(a+b–c)(b+c–a)(c+a–b)]1/3(a+b+c)3≥27[(a+b–c)(b+c–a)(c+a–b)]Hence, the value of (a+b+c)3≥27[(a+b–c)(b+c–a)(c+a–b)]