I came across the following problem that says:
If $x \neq 0,y \neq 0,$ then $x^2+xy+y^2$ is
4.Sometimes positive and sometimes negative.
I have to determine which of the aforementioned options is right.
Now since $x \neq 0,y \neq 0$, so $ x^2+xy+y^2=(x-y)^2+3xy > 0$,if $x,y$ are of same sign. But if $x,y$ are of different sign,I am not sure about the conclusion.
Can someone point me in the right direction? Thanks in advance for your time.