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प्रश्न
Solve:
`2(x^2 + 1/x^2) - (x + 1/x) = 11`
उत्तर
`2(x^2 + 1/x^2) - (x + 1/x) = 11`
Let `x + 1/x = y`
Squaring on both sides
`x^2 + 1/x^2 = y^2 - 2`
Putting these values in the given equation
2(y2 – 2) – y = 11
`=>` 2y2 – 4 – y – 11 = 0
`=>` 2y2 – y – 15 = 0
`=>` 2y2 – 6y + 5y – 15 = 0
`=>` 2y(y – 3) + 5(y – 3) = 0
`=>` (y – 3)(2y + 5) = 0
If y – 3 = 0 or 2y + 5 = 0
Then y = 3 or y =` (-5)/2`
`=> x + 1/x = 3` or `x + 1/x = (-5)/2`
`=> (x^2 + 1)/x = 3` or `(x^2 + 1)/x = (-5)/2`
`=> x^2 - 3x+ 1 = 0` or `2x^2 + 5x + 2 = 0`
`=> x = (-3 +- sqrt((-3)^2 - 4(1)(1)))/(2(1))` or `2x^2 + 4x + x + 2 = 0`
`=> x = (-3 +- sqrt5)/2` or `2x(x + 2) + 1(x + 2) = 0`
Then x = –2 and x = `(-1)/2`
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