If `x ^(4) +(1)/(x ^(4))= 119,` then the value of `x ^(3) - (1)/(x ^(3))` is :

Options

A. `pm 33`
B. 36
C. `-36`
D. `pm 36`

Answer

D

Explanation

`x^4 + 1/x^4 = 119`
`implies x^4 + 1/x^4 + 2x^2 xx 1/x^2 = 121`
`implies (x^2 + (1)/(x^2))^2 = (11)^2`
`implies x^2 + 1/x^2 = 11`
`implies x^2 + 1/x^2 - 2 xx x xx 1/x = 11-2`
`implies (x-1/x)^2= (3)^2`
`implies x- 1/x = pm 3`
`therefore x^3 - 1/x^3 = (3)^3 + 3 xx 3 = 36`
or `(-3)^3 + 3xx (-3) = - 36`
`therefore x^3 - 1/x^3 = pm 36`