Question

Solve: `sqrt(3)x^2 - 2sqrt(2)x - 2sqrt(3) = 0`.

Answer 1

`sqrt(3)x^2 - 2sqrt(2)x - 2sqrt(3) = 0`

⇒ `sqrt(3)x^2 - 3sqrt(2)x + sqrt(2)x - 2sqrt(3) = 0` 

⇒ `sqrt(3)x(x - sqrt(6)) + sqrt(2) (x - sqrt(6)) = 0` 

⇒ `(x - sqrt(6)) (sqrt(3) + sqrt(2)) = 0` 

⇒ `x - sqrt(6) = 0` or `sqrt(3)x + sqrt(2) = 0` 

⇒ `x = sqrt(6)` or `x = -sqrt(2)/sqrt(3) = -sqrt(6)/3` 

Hence, `sqrt(6)` and `-sqrt(6)/3` are the roots of the given equation.