Question

If `x^2 + 1/x^2 = 51, "find"  x - 1/x`

Answer 1

Here, `x^2 + 1/x^2 = 51,`

Using the identity:

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

Substitute the values:

`(x - 1/x)^2` = 51 − 2

`(x - 1/x)^2` = 49

∴ `(x - 1/x) = +-sqrt49`

∴ `(x-1/x) = ±7`