Question

If x² − 4x = 1, find `x^2+1/x^2`.

Answer 1

x² − 4x = 1

Dividing the whole equation by x:

`x^2/x - (4x)/x = 1/x`

∴ The equation will be `x - 4 = 1/x`

Thus,

`x - 1/x = 4`

`4^2 = x^2 + 1/x^2 - 2`   ...`["Using" (x - 1/x)^2 = x^2 + 1/x^2 - 2]`

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

∴ `x^2 + 1/x^2` = 16 + 2

∴ `x^2 + 1/x^2` = 18