Question

Se considera expresia E(x)= $\frac{(x+1)^{2}-4 }{x} : \frac{ x^{2} -x}{ x^{2} }$ , unde x este numar real, x≠0 si x≠1. Determinati numarul real m , m≠0 si m≠1, stiind ca E(m)=5.

Answer 1

E(x)=[(x+1)²-4]/x : (x²-x)/x²
E(x)=[(x+1)²-4]/x : (x²-x)/x²
E(x)=(x+1-2)(x+1+2)/x · x²/x(x-1)
E(x)=(x+1-2)(x+1+2)/x · x²/x(x-1)
E(x)=(x-1)(x+3) /(x-1)
E(x)=(x+3)
x=m
E(m)=(m+3)=5
m=2