ta có: \(\frac{AB}{3}=\frac{AC}{7}=\frac{AB^2}{9}=\frac{AC^2}{49}\)
=> \(\frac{\frac{1}{9}}{\frac{1}{AB^2}}=\frac{\frac{1}{49}}{\frac{1}{AC^2}}\)
mặt khác ta có: \(\frac{1}{AB^2}=\frac{1}{AC^2}=\frac{1}{AH^2}=\frac{1}{42^2}\)
=> \(\frac{\frac{1}{9}}{\frac{1}{AB^2}}=\frac{\frac{1}{49}}{\frac{1}{AC^2}}=\frac{\frac{1}{9}+\frac{1}{49}}{\frac{1}{AB^2}+\frac{1}{AC^2}}\)= \(\frac{\frac{58}{441}}{\frac{1}{42^2}}=232\)
=> \(\hept{\begin{cases}AB^2=2088\\AC^2=11368\end{cases}}\) => \(\hept{\begin{cases}AB=6\sqrt{58}\\AC=14\sqrt{58}\end{cases}}\)
chúc bạn học tốt!! ^^
4574467568568585957345345346565474575676586585768976976976984645645
Ta có: \(\frac{AB}{3}=\frac{AC}{7}\Rightarrow\frac{AB^2}{9}=\frac{AC^2}{49}\Rightarrow\frac{1}{\frac{9}{\frac{1}{AB^2}}}=\frac{1}{\frac{49}{\frac{1}{AC^2}}}\)
Mặt khác, ta có: \(\frac{1}{AB^2}+\frac{1}{AC^2}=\frac{1}{AH^2}=\frac{1}{42^2}\)
\(\Rightarrow\frac{1}{\frac{9}{\frac{1}{AB^2}}}=\frac{1}{\frac{49}{\frac{1}{AC^2}}}=\frac{\frac{1}{9}+\frac{1}{49}}{\frac{1}{AB^2}+\frac{1}{AC^2}}=\frac{58}{\frac{441}{\frac{1}{42^2}}}=232\)
\(\Rightarrow\hept{\begin{cases}AB^2=2088\\AC^2=11368\end{cases}\Rightarrow\hept{\begin{cases}AB=6\sqrt{58}\\AC=14\sqrt{58}\end{cases}}}\)
Đúng không nhể!