Question

If `(x^2 - 1)/x = 7, "find"  x^2 + 1/x^2`

Answer 1

Given: `(x^2 - 1)/x = 7,`

Multiply the equation by x,

x² − 1 = 7x

∴ x² − 7x − 1 = 0

Dividing the equation by x,

`x^2/x - (7x)/x - 1/x = 0/x`

`x - 7 - 1/x = 0`

∴ `x - 1/x = 7`

Using the identity,

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

`(7)^2 = x^2 + 1/x^2 - 2`

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

`49 + 2 = x^2 + 1/x^2`

∴ `51 = x^2 + 1/x^2`

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