\(\left\{{}\begin{matrix}HB\cdot HC=9\\HB+HC=6.15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(6.15-HB\right)\cdot HB=9\\HB+HC=6.15\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}HB^2-6.15HB+9=0\\HB+HC=6.15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}HB=2,4\left(cm\right)\\HC=3.75\left(cm\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}AB=\dfrac{3\sqrt{41}}{5}\left(cm\right)\\AC=\dfrac{3\sqrt{41}}{4}\left(cm\right)\end{matrix}\right.\)
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