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प्रश्न
Solve:
`((3x + 1)/(x + 1)) + ((x + 1)/(3x + 1)) = 5/2`
उत्तर
`((3x + 1)/(x + 1)) + ((x + 1)/(3x + 1)) = 5/2`
Let `(3x + 1)/(x + 1) = 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`
`=> (3x + 1)/(x + 1) = 2` or `(3x + 1)/(x + 1) = 1/2`
`=>` 3x + 1 = 2x + 2 or 6x + 2 = x + 1
`=>` x = 1 or 5x = –1
`=>` x = 1 or x = `(-1)/5`
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