4.47 Let $a, b, c$ be any real numbers that are not all equal. If $x=a^{2}-b c, y=b^{2}-c a, z=c^{2}-a b$, then $x, y, z$
(A) are all not less than 0.
(B) are all not greater than 0.
(C) at least one is less than 0.
(D) at least one is greater than 0.
(China Junior High School Mathematics League, 1994)
[Sol] Notice the algebraic expression
$$
\begin{aligned}
& 2(x+y+z) \\
= & 2\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right) \\
= & (a-b)^{2}+(b-c)^{2}+(c-a)^{2} \\
> & 0,
\end{aligned}
$$

which means $x+y+z>0$, so at least one of $x, y, z$ is greater than 0. Therefore, the answer is $(D)$.