\(x^2+y^2-x-y+1=\left(x^2-x+\frac{1}{4}\right)+\left(y^2-y+\frac{1}{4}\right)+\frac{1}{2}\)
\(=\left(x^2-2.x.\frac{1}{x}+\frac{1}{2^2}\right)+\left(y^2-2.x.\frac{1}{2}+\frac{1}{2^2}\right)+\frac{1}{2}\)
\(=\left(x-\frac{1}{2}\right)^2+\left(y-\frac{1}{2}\right)^2+\frac{1}{2}>0\)(đúng \(\forall x;y\in R\))