Question

If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.

Answer 1

`x + (1)/x = "p", x - (1)/x = "q"`

`(x + 1/x)^2`

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

⇒ p² = `x^2 + (1)/x^2 + 2`

⇒ `x^2 + (1)/x^2 = "p"^2 - 2`     ...(1)

Also, `(x - 1/x)^2`

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

⇒ `"q"^2 = x^2 + (1)/x^2 - 2`

⇒ `x^2 + (1)/x^2 = "q"^2 + 2`    ...(2)

Equating the value `x^2 + (1)/x^2` from and (2), we get :
p² - 2 = q² + 2
⇒ p² - q² = 4.