2022 · Q41
Consider the following equation for the next two (02) items that follow: 6x² - 25x + (6)/(x²) + (25)/(x) + 12 = 0. What is one of the possible values of x - (1)/(x)?
Elementary MathematicsAlgebra
- A1/2
- B3/2
- C2
- D5/2
Explanation
Group as 6(x²+1/x²) − 25(x−1/x) + 12 = 0 and put t = x−1/x, so x²+1/x² = t²+2. Then 6t²−25t+24 = 0, giving t = (25±7)/12 ∈ {8/3, 3/2}. The keyed option is B.