2026 · Q83
For the next two (02) items that follow:
16(x⁴ + 1/x⁴) − 257 = 0
83. What is (x² + 1/x²) equal to?
Elementary MathematicsAlgebra
- A25/16
- B21/16
- C19/4
- D17/4
Explanation
From 16(x⁴+1/x⁴)=257 we get x⁴+1/x⁴=257/16. Then (x²+1/x²)²=257/16+2=289/16, so x²+1/x²=17/4 (positive root), option D. The negative root −17/4 is rejected because x²+1/x²>0 for real x.