$3x^2+y^2-2xy-2\cdot \left(-xy-2y^2+2x^2\right)=$

$3x^2+y^2-2xy+2xy+4y^2-4x^2=5y^2-x^2$

 

$5y^2-x^2=5\cdot {\sqrt{5}}^2-{\left(-2\right)}^2=25-4=21$