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113鳳山高中

1.
已知\(m,n\)為正整數,且\(\sqrt{m}+\sqrt{n}=\sqrt{2023}\),試求數對\(m,n)\)有   組解。
連結有解答,https://math.pro/db/thread-664-1-1.html

3.
已知方陣\(A=\left[\matrix{0&0&-2\cr 1&2&1 \cr 1&0&3}\right]\),\(A^2=\left[\matrix{-2&0&-6\cr 3&4&3 \cr 3&0&7}\right]\)。設\(n\)為正整數,試用\(n\)表方陣\(A^n\)之一般式為   
https://math.pro/db/viewthread.php?tid=661&page=3#pid14875

4.
假設地球為一球體,今以地球球心為原點,地球半徑為單位長,建立一空間直角坐標系。設地球表面上甲、乙、丙三地,甲、乙兩地的座標分別為\((1,0,0)\)及\(\displaystyle \left(\frac{1}{2},\frac{1}{2},\frac{\sqrt{2}}{2}\right)\),丙地為甲乙兩地球面上最短路徑之中點,試求丙地之座標為   
https://math.pro/db/viewthread.php?tid=960&page=1#pid2178

1.
試求\(\left|\matrix{tan40^{\circ}&tan10^{\circ}&tan50^{\circ}\cr tan20^{\circ}&tan50^{\circ}&tan70^{\circ}\cr tan10^{\circ}&tan70^{\circ}&tan80^{\circ}}\right|\)之值。

計算\(\Delta=\left|\matrix{tan70^{\circ}&tan20^{\circ}&tan50^{\circ}\cr tan80^{\circ}&tan10^{\circ}&tan70^{\circ}\cr tan60^{\circ}&tan30^{\circ}&tan30^{\circ}}\right|=\)   
高中數學101 P202

3.
\(f(x)=\sqrt{x-27}+\sqrt{40-x}+\sqrt{x}\),其中\(27<x<40\),試求\(f(x)\)最大值為何?
https://math.pro/db/viewthread.php?tid=661&page=3#pid22174

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