Đáp án:
b=AC=8\(\sqrt{11}\)
c=AB=2\(\sqrt{41}\)
Giải thích các bước giải:
(AB,AC>0)
\(\left\{\begin{matrix} m_{b}^{2}=\frac{2(a^{2}+c^{2})-b^{2}}{4}
& & \\ m_{c}^{2}=\frac{2(a^{2}+b^{2})-c^{2}}{4}
& &
\end{matrix}\right.\)
\(\left\{\begin{matrix} 18^{2}=\frac{2(836+c^{2})-b^{2}}{4}
& & \\ 27^{2}=\frac{2.(836+b^{2})-c^{2}}{4}
& &
\end{matrix}\right.\)
\(\left\{\begin{matrix} 1296=1672+2c^{2}-b^{2}
& & \\ 2916=1672+2b^{2}-c^{2}
& &
\end{matrix}\right.\)
\(\left\{\begin{matrix} b^{2}=2c^{2}+376
& & \\ 2(2c^{2}+376)-c^{2}=1244
& &
\end{matrix}\right.\)
\(\left\{\begin{matrix} b^{2}=2c^{2}+376
& & \\ 3c^{2}=492
& &
\end{matrix}\right.\)
\(\left\{\begin{matrix} b=\sqrt{2(2\sqrt{41})^{2}+376}=8\sqrt{11}
& & \\ c=2\sqrt{41}
& &
\end{matrix}\right.\)
