If x2 - 23x - 1= 0 and x > 1, then the value of x3 - 1/(x^3) will be:

If x² - 23x - 1= 0

Divide by x on both sides,

x -  \(\frac{1}{x}\) = 23

x³ - \(\frac{1}{x^3}\)  = 23³ + 3 × 23 = 12236

 

Note - if x -  \(\frac{1}{x}\) = a

then x³ - \(\frac{1}{x^3}\) =  a³ + 3a