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 - 1/x)^2 = "y"^2`

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

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

m² + 2 - 3(m) - 2 = 0

m² - 3m = 0

m (m - 3) = 0

m = 0 and m - 3 = 0

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

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

= x² - 1 = 0 or x² - 1 = 3x

x² = 1 or x² - 3x - 1 = 0 

x = `sqrt1 or x = (-(-3)±sqrt((-3)^2-4(1)(-1)))/(2(1))`

x = ± 1 or = x = `(3±sqrt13)/2`