Question

Find x from the following equations : `(sqrt(2 - x) + sqrt(2 + x))/(sqrt(2 - x) - sqrt(2 + x)` = 3

Answer 1

`(sqrt(2 - x) + sqrt(2 + x))/(sqrt(2 - x) - sqrt(2 + x)` = 3
Applying componendo and dividendo,

`(sqrt(2 - x) + sqrt(2 + x) + sqrt(2 - x) - sqrt(2 + x))/(sqrt(2 - x) + sqrt(2 + x) - sqrt(2 - x) + sqrt(2 + x)) = (3 + 1)/(3 - 1)`

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

⇒ `sqrt(2 - x)/(sqrt(2 + x)) = (2)/(1)`
Squaring both sides

`(2 - x)/(2 + x) = (4)/(1)`

⇒ 8 + 4x = 2 - x
4x + x = 2
⇒ 5x = –6
∴ x = `(-6)/(5)`.