Notăm [tex]a+2010=x[/tex] și [tex]b+1=y[/tex]
⇒[tex](x+y)^2=xy[/tex] ⇒ [tex] x^{2} +2xy+y^2=xy[/tex] ⇒ [tex]x^2+xy+y^2=0[/tex]
⇒[tex]x^2+xy+ \frac{1}{4}y^2+ \frac{3}{4} y^2=0[/tex]
⇒[tex](x+ \frac{1}{2}y)^2+ \frac{3}{4}y^2=0 [/tex]
⇒[tex] \left \{ {{(x+ \frac{1}{2}y)^2 =0} \atop { \frac{3}{4}y^2 =0}} \right. [/tex] ⇒ [tex]x=y=0[/tex]
⇒[tex] \left \{ {{a+2010=0} \atop {b+1=0}} \right. [/tex] ⇒ [tex] \left \{ {{a=-2010} \atop {b=-1}} \right. [/tex]