If x² + (4 – √3)x – 1 = 0, then what is the value of x² + 1/x²?
A.17 – 8√3
B.21 – 8√3✓ Correct
C.9 – 8√3
D.21 – 12√3
Explanation
From the equation, x + 1/x can be derived. Using x² + (4–√3)x – 1 = 0, dividing by x: x + (4–√3) – 1/x = 0, so x – 1/x = -(4–√3). Then (x–1/x)² = (4–√3)² = 16 – 8√3 + 3 = 19 – 8√3. So x² + 1/x² = (x–1/x)² + 2 = 21 – 8√3.
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