4. Given that $a$ and $b$ are positive numbers, $a+b=3$. For what values of $a$ and $b$ is $\sqrt{a^{2}+4}+\sqrt{b^{2}+25}$ minimized, and what is the minimum value?
( Hint: Refer to Example 5. Answer: The minimum value is $\sqrt{58}$, $\left.a==\frac{6}{7}, b=\frac{15}{7}.\right)$