1. If $4 a-b \sqrt{b-1}=4 a^{2}-\sqrt{b-1}+1$, then among the following four equations:
(1) $2 a+2 b-3=0$,
(2) $(a-b)^{2}+3 a^{2}-b=0$,
(3) $a^{2}+3 a-2 b=0$,
(4) $4 a^{2}+b_{1}^{2}-2 j=0$

which of the following are correct?
(A) 1
(B) 2
(C) 3
(D) 4
-.1.C.
Transform $4 a-b \sqrt{b-1}=4 a^{2}-\sqrt{b-1}+1$ into $(2 a-1)^{2}+(b-1)^{\frac{3}{2}}=0$.
It is found that $a=\frac{1}{2}, b=1$. Substituting these values into the four equations listed, all but (3) hold true.