1. Given the simplest radical form $a \sqrt{2 a+b}$ and $\sqrt{a} \sqrt[b]{7}$ are like radicals, then the values of $a, b$ that satisfy the condition are
(A) do not exist;
(B) there is one set;
(C) there are two sets;
(D) there are more than two sets.
1. (B)

Solution: From $\left\{\begin{array}{l}2 a+b=7 \\ a-b=2\end{array}\right.$, we obtain the unique solution: $\left\{\begin{array}{l}a=3 \\ b=1 .\end{array}\right.$