0;\\
x^2+4y^2-4xy+2x-4y+3=(x^2-4xy+4y^2)+2(x-2y)+3=\\
=(x^2-2\cdot x\cdot2y+(2y)^2)+(x-2y)+3=(x-2y)^2+2(x-2y)+3=\\
\|x-2y=m\|\\
=m^2+2m+3=m^2+2\cdot m+1^2+2=\\
=(m+1)^2+2=(x-2y+1)^2+2;\\
\forall x,y:(x-2y+1)^2\geq0;\\
\forall x,y:(x-2y+1)^2+2>0==>\\==>x^2+4y^2-4xy+2x-4y+3>0
" alt="x^2+4y^2-4xy+2x-4y+3>0;\\
x^2+4y^2-4xy+2x-4y+3=(x^2-4xy+4y^2)+2(x-2y)+3=\\
=(x^2-2\cdot x\cdot2y+(2y)^2)+(x-2y)+3=(x-2y)^2+2(x-2y)+3=\\
\|x-2y=m\|\\
=m^2+2m+3=m^2+2\cdot m+1^2+2=\\
=(m+1)^2+2=(x-2y+1)^2+2;\\
\forall x,y:(x-2y+1)^2\geq0;\\
\forall x,y:(x-2y+1)^2+2>0==>\\==>x^2+4y^2-4xy+2x-4y+3>0
" align="absmiddle" class="latex-formula">