Question

`a = 1/(a - 2). ∴ a - 1/a=` ______.

विकल्प

• 4

• 3

• 2

• 1

Answer 1

`a = 1/(a - 2). ∴ a - 1/a =` 2.

Explanation:

a(a − 2) = 1

a² − 2a − 1 = 0

Using the quadratic formula:

`a = (-(-2) + -sqrt((-2)^2 -  4(1) (-1)))/(2(1))`

`a = (2 + -sqrt(4 + 4))/2`

`a = (2 + -sqrt8)/2`

`a = (2 + -2sqrt2)/2`

`a = 1 + -sqrt2`

Finding, `a - 1/a`

`a - 1/a = (1 + sqrt2) - (-1 + sqrt2)`

`a - 1/a = 1 + sqrt2 + 1 - sqrt2`

`a - 1/a = 1 + 1`

`a - 1/a = 2`