2026 · Q84
For the next two (02) items that follow:
16(x⁴ + 1/x⁴) − 257 = 0
84. What is (x³ + 1/x³) equal to?
Elementary MathematicsAlgebra
- A65/8
- B63/8
- C61/8
- D59/8
Explanation
From the previous item, (x+1/x)²=x²+1/x²+2=25/4, so x+1/x=5/2. Then x³+1/x³=(x+1/x)((x²+1/x²)−1)=(5/2)(13/4)=65/8, option A. The identity x³+1/x³=(x+1/x)³−3(x+1/x) gives the same result: 125/8−15/2=65/8.