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If f(x)=0 is a cubic equation with posit...

If `f(x)=0` is a cubic equation with positive and distinct roots `alpha, beta, gamma` such that `beta` is H.M .of the roots of `f'(x)=0` .If `K= [(2 beta)/(alpha+gamma)]` where [.] represents greatest integer function then find `sum_(i=K)^(5)(2)^(K) `

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