If (x + 1/x) ^2 = 3 what is the value of x^3 + 1/x^3

(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.