49. If $y=\left(m^{2}+2 m\right) x^{m^{2}+m-1}-\sqrt{m+3}$ is a linear function, then the distance between the intercepts of this function's graph with the two coordinate axes is $\qquad$
Answer: $\frac{2}{3} \sqrt{10}$
Solution: Since $y=\left(m^{2}+2 m\right) x^{m^{2}+m-1}-\sqrt{m+3}$ is a linear function,
we have
$$
m^{2}+m-1=1,
$$

Solving this, we get
$$
m=-2 \text {, or } m=1 \text {, }
$$

However, when $m=-2$,
$$
m^{2}+2 m=0,
$$

Therefore, we only take
$$
m=1 \text {. }
$$

The equation of the linear function is $y=3 x-2$, and its graph intersects the two coordinate axes at $\left(\frac{2}{3}, 0\right),(0,-2)$, respectively. The distance between these two intersection points is
$$
\sqrt{\left(\frac{2}{3}\right)^{2}+2^{2}}=\frac{2}{3} \sqrt{10} \text { . }
$$