if α and β are the roots of the quadratic equation x^2 -6x -2 and if an=α n–βn then the value of a10-2a8/a9
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option A(6)......................
Prajal1:
how ?
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since alpha and beta are the roots of the eqn.
x^2-6x-2=0
so, alpha + beta = - b/a
=6
and, alpha * beta = c/a = -2
now a*n=alpha* n - beta* n
a*n = n*(alpha - beta )
a = alpha - beta
= sq.root of (alpha + beta)^2 - 4*alpha* beta
i.e. a = sq.root of 6^2 - 4*(-2)
a = root 44
so, (10*a -2*8a)/9a
put the value of a
we get ; req.ans = (10 -16 root 44) /9root 44.
x^2-6x-2=0
so, alpha + beta = - b/a
=6
and, alpha * beta = c/a = -2
now a*n=alpha* n - beta* n
a*n = n*(alpha - beta )
a = alpha - beta
= sq.root of (alpha + beta)^2 - 4*alpha* beta
i.e. a = sq.root of 6^2 - 4*(-2)
a = root 44
so, (10*a -2*8a)/9a
put the value of a
we get ; req.ans = (10 -16 root 44) /9root 44.
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