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Question
Solve:
`sqrt(x/(x - 3)) + sqrt((x - 3)/x) = 5/2`
Solution
`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
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