Question

If `x^4 + 1/x^4` = 322 and x > 1, then what is the value of `x - 1/x`?

Options

• 6

• 5

• 4

• 3

Answer 1

4

Explanation:

`x^4 + 1/x^4` = 322

⇒ `(x^2)^2 + (1/x^2)^2 + 2x^2 * 1/x^2 = 322 + 2(2 = x^2 * 1/x^2)`  ......(Adding ‘2’ both side)

⇒ `(x^2 + 1/x^2)^2` = 324

∴ `x^2 + 1/x^2` = 18

On subtracting ‘2’ from both side.

⇒ `x^2 + 1/x^2 - 2 = 18 - 2`

⇒ `(x)^2 + (1/x)^2 - 2x 1/x` = 16

⇒ `(x - 1/x)^2` = 16

∴ `x - 1/x` = 4