3. If the equations $x^{2}+2 a x+b^{2}=0$ and $x^{2}+2 c x$ $-b^{2}=0$ have a common root, and $a, b, c$ are the sides of a triangle, then this triangle must be ( ).
(A) right triangle
(B) isosceles triangle
(C) equilateral triangle
(D) isosceles right triangle
3. (A).

Let the common root of the two equations be $m$, then
$$
\begin{array}{l}
m^{2}+2 a m+b^{2}=0, \\
m^{2}+2 c m-b^{2}=0 .
\end{array}
$$

Subtracting the two equations gives
$$
(c-a) m=b^{2} \text {. }
$$

When $c=a$, $b=0$, which is not in line with the problem, so,
$$
c \neq a, m=\frac{b^{2}}{c-a} \text {. }
$$

Substituting $m=\frac{b^{2}}{c-a}$ into either equation and simplifying yields
$$
b^{2}+c^{2}=a^{2} .
$$