if alpha and beta are the roots of the equation 2x2-35x+2=0,then the value of (2 alpha-35)3(2 beta-35)3 is:

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Grade 12th PassAlgebra

if alpha and beta are the roots of the equation 2x²-35x+2=0,then the value of (2 alpha-35)³(2 beta-35)³is:

ASh

8 Years agoGrade 12th Pass

1 Answer

Rajesh Nitharwal

8 Years ago

Alpha and Beta are rootsSo, we have alpha+beta=35/2And. Alpha*beta=2/2=1So, Alpha + 1/alpha =35/2 (also for beta) 2*alpha + 2/alpha =35 2*alpha - 35=(-2/alpha)(2*alpha-35)^3 =-8/(alpha)^3With same process ,we get(2*beta-35)^3 =-8/(beta)^3 Thus (2*alpha-35)^3(2*beta-35)^3=-8/alpha^3 * -8/beta^3 =64/(alpha * beta)^3 =64 (alpha*beta=1)So final answer is 64