命 m=5\sin\theta,
其中 -\frac{\pi}{2}\le\theta\le \frac{\pi}{2}, 将式子化为 s(\theta):=\sqrt{30\cos\theta-30\sin\theta+43}=\sqrt{30\sqrt{2}\cos\left(\theta+\frac{\pi}{4}\right)+43}.\\ 进而就有 \sqrt{13}= s\left(\frac{\pi}{2}\right)\le s(\theta)\le s\left(-\frac{\pi}{4}\right)=5+3\sqrt{2}.\\ }