[tex]a^2+b^2-2a+6b+10=0 \\ \\ (a^2-2a+1)+(b^2+6b+9)=0 \\ \\ (a-1)^2+(b+3)^2=0 \\ \\ (a-1)^2,~(b+3)^2 \geq 0 \Rightarrow (a-1)^2+(b+3)^2 \geq 0,~ \\ \\ dar~(a-1)^2+(b+3)^2=0 \Rightarrow (a-1)^2=0~si~(b+3)^2=0. \\ \\ (a-1)^2=0 \Rightarrow a-1=0 \Rightarrow a=1. \\ \\ (b+3)^2=0 \Rightarrow b+3=0 \Rightarrow b=-3. \\ \\ \underline{Solutie}: (a,b)=(1,-3).[/tex]
