Question 1
It is given that $x,y,z$ are three real numbers such that
$$\frac{x-y}{2+xy}+\frac{y-z}{2+yz}+\frac{z-x}{2+zx}=0.$$
Is it true that at least two of the three numbers must be equal? Justify your answer.
$$\frac{x-y}{2+xy}+\frac{y-z}{2+yz}+\frac{z-x}{2+zx}=0.$$
Is it true that at least two of the three numbers must be equal? Justify your answer.