Question

(a+b+2011)la puterea a doua=(a+2010)(b+1)
Determinati nr a,b E R

Answer 1

Notăm $a+2010=x$ și $b+1=y$

⇒$(x+y)^2=xy$ ⇒ $x^{2} +2xy+y^2=xy$ ⇒ $x^2+xy+y^2=0$

⇒$x^2+xy+ \frac{1}{4}y^2+ \frac{3}{4} y^2=0$

⇒$(x+ \frac{1}{2}y)^2+ \frac{3}{4}y^2=0$

⇒$\left \{ {{(x+ \frac{1}{2}y)^2 =0} \atop { \frac{3}{4}y^2 =0}} \right.$ ⇒ $x=y=0$

⇒$\left \{ {{a+2010=0} \atop {b+1=0}} \right.$ ⇒ $\left \{ {{a=-2010} \atop {b=-1}} \right.$