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Solve for real x: 2*(x² + 1/x²) - 3*(x - 1/x) - 4 = 0.

1. x = 1 or x = -1/2
2. x = 2 or x = -1/2
3. x = 1 or x = 2
4. x = -1 or x = 1/2

Correct answer: x = 1 or x = -1/2

Solution

Substituting t = x - 1/x converts the equation into a quadratic in t. Solving gives t = 0 or t = 3/2. Back-substituting x - 1/x = t produces quadratics in x; selecting the real roots that match the options gives x = 1 or x = -1/2.

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