Question

Please help fast .show that (alpha-beta)² =(alpha+beta)²-4alpha.beta

Answer 1

We can solve this as :

(alpha + beta)^2 = (alpha)^2 + (beta)^2 + 2alpha.beta

(alpha + beta )^2 - 2alpha.beta = (alpha)^2 + (beta)^2 ------------------------(1)

Then ,

(alpha - beta)^2 = (alpha)^2 + (beta)^2 - 2alpha.beta

Put the value from equation 1, we get

(alpha - beta )^2 = (alpha + beta)^2 - 2alpha.beta - 2 alpha.beta

(alpha-beta)^2 = ( alpha+beta)^2 - 4alphabeta

Hence proved .



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