Question

Find all rational numbers, so that the number `(a+sqrt(3))(4-a-sqrt(3))` is rational?

Answer 1

`a=2`

Explanation:

`(a+sqrt3)(4-a-sqrt(3) ) -= 4a-a^2+3 + sqrt(3)(4-2a)`

Hence for this to be rational, there shall be no root 3 in the answer:

Hence to do this `(4-2a) = 0`

`4= 2a => a = 2`