17-183 If the three sides of $\triangle A B C$ are $a, b, c$ and simultaneously satisfy
$$
a^{4}=b^{4}+c^{4}-b^{2} c^{2}, b^{4}=c^{4}+a^{4}-a^{2} c^{2} \text {. }
$$

then $\triangle A B C$ is
(A) a scalene triangle.
(B) an equilateral triangle.
(C) a right triangle.
(D) an obtuse triangle.
(E) an isosceles right triangle.
(China Junior High School Mathematics Correspondence Competition, 1985)
［Solution］From the given, we have
$$
\left\{\begin{array}{l}
a^{4}-b^{4}=c^{4}-b^{2} c^{2}, \\
b^{4}-a^{4}=c^{4}-a^{2} c^{2},
\end{array}\right.
$$

Thus, $2 c^{4}=\left(a^{2}+b^{2}\right) c^{2}$, so
$$
a^{2}+b^{2}=2 c^{2} \text {. }
$$

Substituting (3) into (1) and (2), we get
$$
a^{2}+c^{2}=2 b^{2}, \quad b^{2}+c^{2}=2 a^{2},
$$

Therefore, $a=b=c$. Hence, $\triangle A B C$ is an equilateral triangle. The answer is $(B)$.