Question

If `(x^2 + 1)/x = 5, "find"  x^2 + 1/x^2`

Answer 1

Given: `(x^2 + 1)/x = 5,`

Multiply the equation by x,

x² + 1 = 5x

∴ x² − 5x + 1 = 0

Dividing the equation by x,

`x^2/x - (5x)/x + 1/x = 0/x`

`x - 5 + 1/x = 0`

∴ `x + 1/x = 5`

Using the identity,

`x^2 + 1/x^2 = (x + 1/x)^2 − 2`

`x^2 + 1/x^2` = (5)² − 2

`x^2 + 1/x^2` = 25 − 2

∴ `x^2 + 1/x^2` = 23