Question

Solve:

`(x^2 + 1/x^2) - 3(x - 1/x) - 2 = 0`

Answer 1

`(x^2 + 1/x^2) - 3(x - 1/x) - 2 = 0`

Let `x - 1/x = y`

Squaring on both sides

`x^2 + 1/x^2 - 2 = y^2`

`=> x^2 + 1/x^2 = y^2 + 2`

Putting these values in the given equation

(y² + 2) – 3y – 2 = 0

`=>` y² – 3y = 0

`=>` y(y – 3) = 0

If y = 0 or y – 3 = 0

Then y = 0 or y = 3

`=> x - 1/x = 0` or `x - 1/x = 3`

`=> (x^2 - 1)/x = 0` or `(x^2 - 1)/x = 3`

`=> x^2 - 1 = 0` or `x^2 - 3x - 1 = 0`

`=> (x + 1)(x - 1) = 0` or `(-(-3) +- sqrt((-3)^2 - 4(1)(-1)))/(2(1))`

`=> x = -1` and `x = 1` or `x = (3 +- sqrt13)/2`