Докажите неравенство 10x^2-6xy+y^2-4x+6>0.

\[10x^{2} - 6xy + y^{2} - 4x + 6 > 0\]

\[\left( 9x^{2} - 6xy + y^{2} \right) + \left( x^{2} - 4x + 4 \right) + 2 > 0\]

\[\underset{\geq 0}{\overset{(3x - y)^{2}}{︸}} + \underset{\geq 0}{\overset{(x - 2)^{2}}{︸}}\underset{> 0}{\overset{+ 2}{︸}} > 0 \Longrightarrow верно.\]