Question

Solve the following equation by using formula :

`(x - 2)/(x + 2) + (x + 2)/(x - 2)` = 4

Answer 1

`(x - 2)/(x + 2) + (x + 2)/(x - 2)` = 4

⇒ `((x - 2)^2 + (x + 2)^2)/((x + 2)(x - 2)` = 4

⇒ `(x^2 - 4x + 4 + x^2 + 4x + 4)/(x^2 - 4)`
⇒ 2x² + 8 = 4x² - 16
⇒ 2x² + 8 - 4x² + 16 = 0
⇒ -2x² + 24 = 0
⇒ x² - 12 = 0
Here a = 1, b = 0, c = -12
D = b² - 4ac
= (0)² - 4 x 1(-12)
= 0 + 48
= 48

∵ x = `(-b ± sqrt("D"))/(2a)`

= `(0 ± sqrt(48))/(2 xx 1)`

= `(±sqrt(48))/(2)`

= `(±sqrt(16 xx 3))/(2)`

= `± (4sqrt(3))/(2)`
= ±`2sqrt(3)`
Hence roots are `2sqrt(3), -2sqrt(3)`.