Any $(x, y, z)$ can satisfy the $5x^2+2y^2+6z^2-6xy-2xz+2yz<0$? Please tell me whether there any $(x, y, z)$ 
which can satisfy the $5x^2+2y^2+6z^2-6xy-2xz+2yz<0$ ?
No process or just solve it by calculator are both fine.
Thank you.

The expression $$5x^2+2y^2+6z^2-6xy-2xz+2yz$$ may be written as $$3(x-y)^2+(x-z)^2+(y+z)^2+x^2-2y^2+4z^2$$ Notice that the only term with a negative sign is $-2y^2$, all others are positive. Setting $x=z=0$ we have $$3(x-y)^2+(x-z)^2+(y+z)^2+x^2-2y^2+4z^2\geq2y^2\geq 0$$
Hence, the expression is never negative.
