Question

Using properties of proportion, solve for x:

`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`

Answer 1

`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`

Applying componendo and dividendo,

`(3x + sqrt(9x^2 - 5) + 3x - sqrt(9x^2 - 5))/(3x + sqrt(9x^2 - 5) - 3x + sqrt(9x^2 - 5)) = (5 + 1)/(5 - 1)`

`(6x)/(2sqrt(9x^2 - 5)) = 6/4`

`(3x)/sqrt(9x^2-5) = 3/2`

`x/sqrt(9x^2 - 5) = 1/2`

Squaring both sides,

`x^2/(9x^2 - 5) = 1/4`

`4x^2 - 9x^2 = - 5`

`-5x^2 = -5`

`5x^2 = 5`

`x^2 = 1`

`x= sqrt1`

x = 1