Question

If x4 + 1/x power 4 = 119, then find the value of x-1/x.

Answer 1

(x^2+1/x^2)^2 -2 = x^4+1/x^4
x^2+1/x^2=11
(x-1/x)^2+2=x^2+1/x2
x-1/x=3

Answer 2

Given, x4 + 1/x^4 = 119

We know that a^4 + b^4 = (a^2 + b^2)^2 - 2a^2b^2

                     x^4 + (1/x^4) = (x^2+1/x^2) - 2 * (x)^2 * (1/x)^2
 
                    x^4 + (1/x^4) = (x^2+1/x^2) - 2

                    119 = (x^2+1/x^2) - 2

                     (x^2+1/x^2) = 119 + 2 

                     (x^2+1/x^2) =  121

 We know that (a^2 + b^2 = (a-b)^2 + 2ab)

                     (x^2 - 1/x^2) +2 = 11

                     (x^2 - 1/x^2) = 9

                     x - 1/x = 3.


Hope this helps!