Answered

svp aidez moi c'est pour demain (x+1/x)²=7 alors x^3+1/X^3=?

Sagot :

(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