3. Let the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a>1, b>1)$ have a focal distance of $2 c$, and let the line $l$ pass through the points $(a, 0)$ and $(0, b)$. If the distance from the point $(1, 0)$ to the line $l$ plus the distance from the point $(-1,0)$ to the line $l$ is $S \geqslant \frac{4 c}{5}$. Then the range of the eccentricity $e$ of the hyperbola is