Sum
Solve `2(x^2 + 1/x^2) - (x + 1/x) = 11`
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Solution
`2(x^2 + 1/x^2) - (x + 1/x) = 11`
Let `x + 1/x = y`
squaring on both side
`x^2 + 1/x^2 = y^2 - 2`
Putting these values in the given equation
`2(y^2 - 2) - y = 11`
``=> 2y^2 - 4 - y - 11 = 0`
`=> 2y^2 - y - 15 = 0`
`=> 2y^2 - 6y + 5y - 15 = 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`
Concept: Quadratic Equations
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