Question

Using componendo and idendo, 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)`
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) = (10)/(8) = (5)/(4)`
`(2sqrt(3x + 4))/(2sqrt(3x - 5)) = (5)/(4)`
⇒ `(3x + 4)/(3x - 5) = (25)/(16)   ...("squaring both sides")`
48x + 64 = 75x - 125
⇒  75x - 48x = 125 + 64
27x = 189
⇒  x = `(189)/(27)`
= 7.