回復 1# 瓜農自足 的帖子
\(\begin{align}
& {{x}^{2}}+{{y}^{2}}=1 \\
& {{\left( -3x+4y \right)}^{2}}\le \left[ {{\left( -3 \right)}^{2}}+{{4}^{2}} \right]\left( {{x}^{2}}+{{y}^{2}} \right)=25 \\
& -5\le -3x+4y\le 5 \\
\end{align}\)
Z之最大值為20，最小值為10
所求\(=\sqrt{{{\left( 20-10 \right)}^{2}}+{{2}^{2}}}=2\sqrt{26}\)
要求出A和B的座標只要解以下的聯立方程
\(\begin{align}
& \left\{ \begin{align}
& 20=-3x+4y+15 \\
& \frac{-3}{x}=\frac{4}{y} \\
\end{align} \right. \\
& \left\{ \begin{align}
& 10=-3x+4y+15 \\
& \frac{-3}{x}=\frac{4}{y} \\
\end{align} \right. \\
\end{align}\)
