Question

Find x from the following equations : `(sqrt(12x + 1) + sqrt(2x - 3))/(sqrt(12x + 1) - sqrt(2x - 3)) = (3)/(2)`

Answer 1

`(sqrt(12x + 1) + sqrt(2x - 3))/(sqrt(12x + 1) - sqrt(2x - 3)) = (3)/(2)`
Applying componendo and dividendo,
`(sqrt(12x + 1) + sqrt(2x - 3) + sqrt(12x + 1) - sqrt(2x - 3))/(sqrt(2x + 1) + sqrt(2x - 3) - sqrt(12x + 1) + sqrt(2x - 3)) = (3 + 2)/(3 - 2)`

⇒ `(2sqrt(12x + 1))/(2sqrt(2x - 3)) = (5)/(1)`

⇒ `(sqrt(12x + 1))/(sqrt(2x - 3)) = (5)/(1)`
Squaring both sides,
`(12x + 1)/(2x - 3) = (25)/(1)`

⇒ 50x – 75 = 12x + 1
⇒  50x – 12x = 1 + 75
⇒  38x = 76
⇒ x = `(76)/(38)` = 2
∴ x = 2.