Đáp án:
$\left[\begin{array}{l} \left\{\begin{array}{l} AB=4\\ AC=3\end{array} \right.\\ \left\{\begin{array}{l} AB=3\\ AC=4\end{array} \right.\end{array} \right.$
Giải thích các bước giải:
$\Delta ABC$ vuông tại $A$, đường cao $AH$
$\Rightarrow \left\{\begin{array}{l} AB^2+AC^2=BC^2\\ AB.AC=AH.BC\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} AB^2+AC^2=25\\ AB.AC=12\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} AB^2+\left(\dfrac{12}{AB}\right)^2=25\\ AC=\dfrac{12}{AB}\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} AB^4-25AB^2+144=0\\ AC=\dfrac{12}{AB}\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} \left[\begin{array}{l} AB^2=16\\ AB^2=9\end{array} \right.\\ AC=\dfrac{12}{AB}\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} \left\{\begin{array}{l} AB=4\\ AC=3\end{array} \right.\\ \left\{\begin{array}{l} AB=3\\ AC=4\end{array} \right.\end{array} \right.$
