Question

Solve the following equation by using formula :

`sqrt(3)x^2 + 10x - 8sqrt(3)` = 0

Answer 1

`sqrt(3)x^2 + 10x - 8sqrt(3)` = 0
Here `a = sqrt(3), b = 10, c = -8sqrt(3)`
D = b² - 4ac
= `(10)^2 - 4 xx sqrt(3) xx (-8sqrt(3))`
= 100 + 96
= 196

∵ x = `(-b ± sqrt("D"))/(2a)`

= `(-10 ± sqrt(196))/(2 xx sqrt(3))`

= `(-10 ± 14)/(2sqrt(3)`

∴ x₁ = `(-10 + 14)/(2sqrt(3)`

= `(4)/(2sqrt(3)`

= `(2 xx sqrt(3))/(sqrt(3) xx sqrt(3)`

= `(2sqrt(3))/(3)`

x₂ = `(-10 - 14)/(2sqrt(3)`

= `(-24)/(2sqrt(3)`

= `(-12 xx sqrt(3))/(sqrt(3) xx sqrt(3)`

= `(-12sqrt(3))/(3)`
= `-4sqrt(3)`

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