Question

se considera expresia E(x)=x ²+4x+4 totul supra x(x+2)si toata fractia :(1+2/x),unde x este numar real,x≠-2 si x≠0.Aratati ca E(x)=1 pentru orice x numar real,x≠-2 si x≠0,dau 20 de puncte,vA ROGGGGGGGGGGGGGGGGG!!!!!!!!

Answer 1

[tex] \frac{x^2+4x+4}{x^2+2x}:1+ \frac{2}{x} [/tex]

[tex] \frac{x^2+4x+4}{x(x+2)}: \frac{x+2}{x}= [/tex]

[tex]x^2+4x+4=0 a=1 b=4 c=4 delta=b^2-4ac = 4^2-4*1*4=16-16=0 [/tex]

Cand delta este 0 avem o radacina

$x1= \frac{-4+0}{2}= \frac{-4}{2}=-2$

Conform formulei $a(x-x1)(x-x2)$

$x^2+4x+4= (x+2)(x+2)$

$\frac{(x+2)(x+2)}{x(x+2)}* \frac{x}{x+2} = 1$

Se reduc