Question

Solve the following equation by factorization

`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0

Answer 1

`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0
`{4sqrt(3) xx (-2sqrt(3)) = 8xx (-3) = -24}`
`4sqrt(3)x^2 + 8x - 3x - 2sqrt(3)` = 0
⇒ `4x (sqrt(3)x + 2) - sqrt(3)(sqrt(3)x + 2)` = 0
⇒ `(sqrt(3)x + 2) (4x - sqrt(3))` = 0
Either `sqrt(3)x + 2` = 0,
then `sqrt(3)x` = -2

⇒ x = `-(2)/sqrt(3)`

⇒ x = `(-2 xx sqrt(3))/(sqrt(3) xx sqrt(3))`

= `(-2sqrt(3))/(3)`
or
`4x - sqrt(3)` = 0,
then `4x = sqrt(3)`

⇒ x = `sqrt(3)/(4)`

Hence x = `(-2sqrt(3))/(3), sqrt(3)/(4)`.