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If f (x) = 27x^(3) -(1)/(x^(3)) and alph...

If `f (x) = 27x^(3) -(1)/(x^(3))` and `alpha, beta` are roots of `3x - (1)/(x) = 2` then

A

`f (alpha) = f(beta)`

B

`f(alpha) =10`

C

`f (beta) = -10`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x) =27 x^(3) -(1)/(x^(3)) = (3x-(1)/(x))^(3) + 9(3x-(1)/(x))`
Since `alpha ` and `beta` are the roots of `3x -(1)/(x) =2`
`therefore 3 alpha - (1)/(alpha) = 2` and `3beta -(1)/(beta) =2`
Now,
`f(alpha) = (3alpha -(1)/(3))^(3) + 9 (3alpha -(1)/(alpha))=2^(3) + 9xx 2 = 26`
Similarly, we have `f (beta) = 26`
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