2023 · Q21
If α and β are the roots of the equation x² - 7x + 1 = 0, then what is the value of α⁴ + β⁴?
Elementary MathematicsAlgebra
- A2207
- B2247
- C2317
- D2337
Explanation
From the equation, α + β = 7 and αβ = 1. Then α² + β² = 49 − 2 = 47, and α⁴ + β⁴ = (α² + β²)² − 2(αβ)² = 2209 − 2 = 2207 (A).