2023 · Q77
If x = 6/(7 − 6/(7 − 6/(7 − ...))); x > 1, then what is the value of x² − 3x + 2 equal to?
Elementary MathematicsAlgebra
- A0
- B1
- C18
- D20
Explanation
If the infinite continued fraction converges to x, then x = 6/(7 − x). This gives x(7 − x) = 6, i.e. x² − 7x + 6 = 0, so (x − 1)(x − 6) = 0. Since x > 1, x = 6. Then x² − 3x + 2 = 36 − 18 + 2 = 20. The answer is (D).