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Solve the question no vi and vii from the above attachment
Here, let a+b+c = Kso, Required to prove :a/K-a + b/K-b + c/K-c > 3/2Now, the function f(x)=x/K-x is a concave function since f’’(x) > 0 when x > 0 . So, applying JENSEN’S INEQUALITY,f(a) + f(b) + f(c) > 3f((a+b+c)/3) = 3× (a+b+c/3)/ K – (a+b+c/3)putting K=a+b+c ,we get,f(a) + f(b) + f(c) > 3/2 (PROVED)
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