voici un exercice de mon dm de math il me parait simple mais je suis bloqué (x+1/x)²=7,alors x^3+1/x^3=?

(x+1/x)²=7

donc x²+2*x*1/x+1/x²=7

donc x²+1/x²=5 et x+1/x=√7

or (x+1/x)³=x³+3*x²*1/x+3*x²*1/x+1/x³

                  =x³+3(x+1/x)+1/x³

ainsi x³+1/x³=(x+1/x)³-3(x+1/x)

                      =(√7)³-3*√7

                      =7√7-3√7

                      =4√7