Question

Using properties of proportion solve for x, given

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

Answer 1

`(sqrt(5x)+sqrt(2x -6))/(sqrt(5x)- sqrt(2x -6)) = 4/1`

Using componendo and dividendo on both sides

We know, if `a/b = c/d ⇒ (a+b)/(a- b)= ( c+ d) /( c- d) `

` ∴ ((sqrt(5x) + sqrt(2x -6)) + ( sqrt(5x) - sqrt(2x -6) ))/((sqrt(5x) + sqrt(2x - 6)) - (sqrt(5x) - sqrt(2x -6 ))) = (4+1)/(4-1)`

`sqrt(5x)/(sqrt(2x -6)) = 5/3`

On squaring both sides

`(5x)/(2x- 6) = 25/9`

45 x = 50x - 150 

 150 = 5x 

`⇒ x = 150/5`

⇒ x = 30