Verified answer

Answer

`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)`.