Question

Using properties of proportion, solve for x. Given that x is positive:

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

Answer 1

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

`=> (2x + sqrt(4x^2 -1) + 2x  - sqrt(4x^2 - 1))/(2x + sqrt(4x^2 - 1) - 2x +  sqrt(4x^2 - 1)) = (4+1)/(4-1) `     (By componendo dividendo)

`=> (4x)/(2sqrt(4x^2 -1)) = 5/3`

`=> (2x)/(sqrt(4x^2 -1)) = 5/3`

`=> (4x^2)/(4x^2 -1) = 25/9`    (squaring both sides)

`=>(4x^2 - 4x^2 + 1)/(4x^2 -1) = (25-9)/9`    (By dividendo)

`=> 1/(4x^2 -1)  = 16/9`

`=> 9 = 64x^2 - 16`

`=> 64x^2 = 25`

`=> x^2 = 25/64`

`=> x = +- 5/8`

`=> x = 5/8`   (x is positive)