Question

Using properties of proportion, find the value of x from the following:

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

Answer 1

We are given that

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

Apply Componendo and Dividendo,

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

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

⇒ `sqrt(12x + 1)/sqrt(2x - 3) = 5`

Squaring both sides,

⇒ `(12x + 1)/(2x - 3) = 25`

⇒ 12x + 1 = 25(2x − 3)

⇒ 12x + 1 = 50x − 75

⇒ 76 = 38x

⇒ x = `76/36`

⇒ x = 2