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The ubiquitous AM-GM inequality has many applications. It almost crops up in unlikely situations and the solutions using AM-GM aretruly elegant . Recall that for n positive reals a_(i) I = 1,2 …,n, the AM-GM inequality tells (overset(n) underset(1)suma_i)/n ge ( overset(n)underset(1)proda_i)^((1)/(n)) The special in which the inequality turns into equality help solves many problems where at first we seem to have not informantion to arrive at the answer . If a,b,c are positive integers satisfying (a)/(b+c)+(b)/(c+a) + (c)/(a+b) = (3)/(2), then the value of abc + (1)/(abc) |
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