Question

If `x^2-(a + 1/a) x + 1 = 0` then the values of x are ______.

Options

• a, a

• `1/a, 1/a`

• `a, 1/a`

• `-a, -1/a`

Answer 1

If `x^2-(a + 1/a) x + 1 = 0` then the values of x are `\underline(a, 1/a)`.

Explanation:

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

ax² + bx + c = 0

a = 1, 

b = `-(a+1/a)`

c = 1

We look for factors whose sum is `(a+1/a)` and product is 1:

`(x-a)(x-1/a) = 0`

x − a = 0 or `(x-1/a) = 0` 

x = a and `x=1/a`