#1 明野提到的數學問題
發表於 : 2022年 4月 23日, 21:04
看似複雜，實則簡易：
\(\begin{align}
\sqrt{X}+\sqrt{-X}&=2 \\
(\sqrt{X}+\sqrt{-X})^2&=2^2 \\
(\sqrt{X}+\sqrt{-X})^2&=2^2 \\
X+2\cdot\sqrt{X}\cdot\sqrt{-X}-X&=4 \\
\sqrt{X}\cdot\sqrt{-X}&=2 \\
\left|X\right|\cdot\textit{i}&=2 \\
\left|X\right|\cdot\textit{i}\cdot\textit{i}&=2\cdot\textit{i} \\
\left|X\right|\cdot-1&=2\cdot\textit{i} \\
-1\left|X\right|&=2\textit{i} \\
X&=\pm2\textit{i}\end{align}\)
\(\begin{align}
\sqrt{X}+\sqrt{-X}&=2 \\
(\sqrt{X}+\sqrt{-X})^2&=2^2 \\
(\sqrt{X}+\sqrt{-X})^2&=2^2 \\
X+2\cdot\sqrt{X}\cdot\sqrt{-X}-X&=4 \\
\sqrt{X}\cdot\sqrt{-X}&=2 \\
\left|X\right|\cdot\textit{i}&=2 \\
\left|X\right|\cdot\textit{i}\cdot\textit{i}&=2\cdot\textit{i} \\
\left|X\right|\cdot-1&=2\cdot\textit{i} \\
-1\left|X\right|&=2\textit{i} \\
X&=\pm2\textit{i}\end{align}\)