Question

Using componendo and dividendo, find the value of x

`(sqrt(3x + 4) + sqrt(3x -5))/(sqrt(3x + 4)-sqrt(3x - 5))  = 9`

Answer 1

`(sqrt(3x + 4) + sqrt(3x -5))/(sqrt(3x + 4)-sqrt(3x - 5))  = 9`

Using componendo and dividendo,

`(sqrt(3x + 4) + sqrt(3x - 5) + sqrt(3x + 4) - sqrt(3x - 5))/(sqrt(3x + 4) + sqrt(3x - 5) - sqrt(3x + 4) + sqrt(3x - 5)) = (9+1)/(9-1)`

`=> (2sqrt(3x + 4))/(2sqrt(3x - 5)) = 10/8`

`=> sqrt(3x + 4)/(sqrt(3x -5)) = 5/4`

Squaring both sides,

`=> (3x + 4)/(3x - 5) = 25/16`

`=>16(3x + 4) = 25(3x - 5)`

`=> 48x + 64 = 75x - 125`

`=> 75x - 48x = 64 + 125`

`=> 27x = 189`

`=> x = 7`