9. Let $1<b<\frac{5}{4}$, the number of distinct real roots of the equation $\left|x^{2}-1\right|=x+b$ is

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9. Let $1<b<\frac{5}{4}$, the number of distinct real roots of the equation $\left|x^{2}-1\right|=x+b$ is
9. 4.

Draw the graphs of $y=\left|x^{2}-1\right|$ and $y=x+b$. When the line $y=x+b$ moves, if $b=\frac{5}{4}$, the line is tangent to the curve; when $b=1$, there are two intersection points; and when $1<b<\frac{5}{4}$, there are four intersection points.