Question

Solve the following quadratic equation:

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

Answer 1

We write, `-2sqrt(2)x = -3sqrt(2)x + sqrt(2)x` as `sqrt(3)x^2 xx (-2sqrt(3)) = -6x^2 = (-3sqrt(2)x) xx (sqrt(2)x)`

∴ `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)x + sqrt(2)) = 0` 

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

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

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