(x + 1/x)² = 3 | √
x + 1/x = √3
According to short multiplication formula:
(a + b)³ =a³ + 3a²b + 3ab² + b³
x³ + 1/x³ = (x)³ + (1/x)³ = (x + 1/x)³ - 3x²/x - 3x/x² =
= (x + 1/x)³ - 3x - 3/x = (x + 1/x)³ - 3(x + 1/x) =
= (√3)³ - 3√3 = 3√3 - 3√3 = 0
If (x + 1/x)² = 3 the value of x³ + 1/x³ is 0.
