Question

a la a 2 +4a-2b+b la a 2=-5
Calculati (a+b)totul la 2010+b la 2010

Answer 1

[tex]a^2+4a-2b+b^2=-5\\ a^2+4a+b^2-2b+5=0\\ (a^2+4a+4)+(b^2-2b+1)=0\\ (a+2)^2+(b-1)^2=0\\ Dar: (a+2)^2+(b-1)^2\geq 0,\text{ceea ce implica:}\\ \left \{ {{a+2=0} \atop {b-1=0}} \right. \Leftrightarrow \left \{ {{a=-2} \atop {b=1}} \right. \\ (a+b)^2+b^{2010}=(-2+1)^{2010}+1^{2010}=(-1)^{2010}+1=1+1=\boxed{2}[/tex]