If x2 - 2x + 1= 0 and x > 1, then the value of x3 + 1/(x^3) will be:

If x² - 2x + 1= 0

Divide by x on both sides,

x +  \(\frac{1}{x}\) = 2

x³ + \(\frac{1}{x^3}\)  = 2³ - 3 × 2 = 2

 

Note - if x +  \(\frac{1}{x}\) = a

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