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If x^4 + 1/(x^4) = 119 and x > 1. Then f...

If `x^4 + 1/(x^4) = 119 and x > 1`. Then find the positive value of `x^3 - 1/(x^3)` .

A

25

B

27

C

36

D

49

Text Solution

Verified by Experts

The correct Answer is:
C
`x^4 + 1/x^4 = 119`
`(x^2 + 1/x^2)^2 - 2 = 119`
`implies (x^2 + 1/x^2)^2 = 121`
`implies x^2 + 1/x^2 + 11`
`implies (x - 1/x)^2+ 2 = 11`
`implies x - 1/x = 3`
`therefore x^3 - 1/x^3 = (x- 1/x)^3 + 3(x-1/x)`
`= (3)^3 + 3(3)`
= 27 + 9 = 36
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