Question

Solve:

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

Answer 1

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

Let `sqrt(x/(x -3)) = y`

Then `y + 1/y = 5/2`

`=> (y^2 + 1)/y = 5/2`

`=>` 2y² + 2 = 5y

`=>` 2y² – 5y + 2 = 0

`=>` 2y² – 4y – y + 2 = 0

`=>` 2y(y – 2) – 1(y – 2) = 0

`=>` (y – 2)(2y – 1) = 0

If y – 2 = 0 or 2y – 1 = 0

Then y = 2 or y = `1/2`

`=> sqrt(x/(x -3)) = 2` or `sqrt(x/(x -3)) = 1/2`

`=> x/(x - 3) = 4` or `x/(x - 3) = 1/4`

`=>` x = 4 or x = –1