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)) = 9/1`

Applying componendo and dividend, we have

`(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)) = 5/4`

Squaring both sides, we have

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

`=>` 16(3x + 4) = 25(3x – 5)

`=>` 48x – 64 = 75x – 125

`=>` 75x – 48x = 64 + 125

`=>` 27x = 189

`=> x = 189/27`

`=>` x = 7