If x4 - 62x2 + 1 = 0, then a value of x3 + x-3 can be:
2020
If x4 - 62x2 + 1 = 0, then a value of x3 + x-3 can be:
- A.
389
- B.
488
- C.
498
- D.
320
Attempted by 8 students.
Show answer & explanation
Correct answer: B
Key idea: Divide by x² to form x² + x⁻², then use the identity for x³ + x⁻³.
x⁴ - 62x² + 1 = 0. Dividing by x² gives x² + x⁻² = 62.
So (x + x⁻¹)² = x² + 2 + x⁻² = 64, hence x + x⁻¹ = 8 or -8.
Using x³ + x⁻³ = (x + x⁻¹)³ - 3(x + x⁻¹), one possible value is 8³ - 3×8 = 488.
Answer: Option 1, 488, is correct.