If x⁴ − 79x² + 1 = 0, then a value of x³ + x⁻³ can be:

Given:
x⁴ − 79x² + 1 = 0
We need to find the value of:
x³ + x⁻³
Step 1: Divide the equation by x²
x⁴/x² − 79x²/x² + 1/x² = 0
x² + 1/x² = 79
Step 2: Use identity
(x + 1/x)² = x² + 1/x² + 2
Substitute:
(x + 1/x)² = 79 + 2
= 81
x + 1/x = 9
Step 3: Use another identity
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x)
Substitute:
= 9³ − 3 × 9
= 729 − 27
= 702