Question

Va rooog e urgent imi trebuie luni la scoala:                                                                           Daca x+1/x=4, calculati x²+1/x² si x³+1/x³

Answer 1

Daca ridici la patrat prima relatie (x+1/x)^2=16, deci x^2+2x*1/x +1/x^2=16, x^2+2+1/x^2=16, x^2+1/x^2=14
Prin inmultirea (x+1/x)*(x^2+1/x^2)=56, deci x^3+x^2*1/x+1/x^2*x + 1/x^2* 1/x=56, x^3+x+1/x+1/x^3=56 si cum x+1/x=4 rezulta x^3+1/x^3=52