\(AI=\sqrt{\left(1-1\right)^2+\left(1+3\right)^2+\left(0-2\right)^2}=\sqrt{20}\left(km\right)\)
\(BI=\sqrt{\left(m-1\right)^2+\left(m-2-1\right)^2+\left(6-0\right)^2}=\sqrt{2m^2-8m+46}\left(km\right)\)
\(CI=\sqrt{\left(m-2-1\right)^2+\left(m-1\right)^2+\left(5-0\right)^2}=\sqrt{2m^2-8m+35}\left(km\right)\)
Để khoảng cách từ mỗi drone đến kho hàng không vượt quá \(100\left(km\right)\)
\(\left\{{}\begin{matrix}AI=\sqrt{20}\le100\left(đúng\right)\\BI=\sqrt{2m^2-8m+46}\le100\\AI=\sqrt{2m^2-8m+35}\le100\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2m^2-8m+46\le10000\\2m^2-8m+35\le10000\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}m^2-4m+23\le5000\\m^2-4m+\dfrac{35}{2}\le5000\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(m-2\right)^2\le4981\\\left(m-2\right)^2\le4991,5\end{matrix}\right.\) \(\Leftrightarrow\left(m-2\right)^2\le4981\)
\(\Leftrightarrow-\sqrt{4981}+2\le m\le\sqrt{4981}+2\)
\(\Rightarrow m\in\left[0;1;2;...;72\right]\) \(\Rightarrow\) có \(73\) giá trị \(m\in Z^+\) thỏa mãn đề bài
