Question

if x + 1/x=4 find the value of x3-1/x3​

Answer 1

x + 1/x=4

squaring both sides

(x + 1/x)² = 16

(x - 1/x)² + 4 = 16

(x - 1/x)² = 12

x - 1/x = 2√3

cubing both sides

(x - 1/x)³ = (2√3)³

x³ - 1/x³ - 3(x-1/x) = 24√3

x³ - 1/x³ - 3×2√3 = 24√3

x³ - 1/x³ - 6√3 = 24√3

x³ - 1/x³ = 30√3