Question

If x³-1/x³=14, then x-1/x=

Answer 1

Given

x^3 - 1/x^3 = 14

And you that (a-b)^3 = a^3 -b^3 -3ab (a - b)…(1)

So according to equation (1) you will have

(x - 1/x)^3 = x^3 - 1/x^3 - 3×x×(1/x) ( x-1/x)

=> (x - 1/x)^3 + 3( x-1/x) - 14 = 0………..(2)

Let m = (x - 1/x) so putting the value of m in equation (2) you will get

m^3 + 3m - 14 = 0 ……..(3)

By hit and trail on putting m = 2 you will find that it is the root of the above equation (3)

Therefore,
x-1/x=2