if $a,b$ such $a^2+b^2+4=2a+ab+2b$,find $a^2b$ let $a,b\in R$, and such
$$a^2+b^2+4=2a+ab+2b$$
Find $a^2b=?$
My idea: $$a^2-2a+1+b^2-2b+1+2+ab=0$$
$$(a-1)^2+(b-1)^2+ab+2=0$$
then I can't it
maybe this problem   can use inequality to solve it,Than you 

You can look at the problem as the solution of a quadratic equation in $a$. The solutions are $$a_{\pm}=1+\frac{1}{2} \left(b\pm \sqrt{3} \sqrt{-(b-2)^2}\right)$$ Since $a,b\in R$, $b$ must be equal to $2$; then $a=2$.
