本帖最后由 青青子衿 于 2020-2-22 22:17 编辑
$\color{black}{a^2+b^2=2(c^2+d^2)}$
https://math.stackexchange.com/questions/2847898/
\begin{align*}
&\color{black}{\left\{
\begin{split}
a&=2mp+2np+nq\\
b&=2mp+2mq+nq\\
c&=2mp+\phantom{1}mq+np\\
d&=\phantom{1}mq+\,\,\phantom{1}np+nq
\end{split}
\right.}\\
\\
&\color{black}{\left\{
\begin{split}
a&=mp+mq-np+nq\\
b&=mp-mq+np+nq\\
c&=mp-nq\\
d&=mq+np
\end{split}
\right.}
\end{align*}
...- a^2 + b^2 - 2 c^2 - 2 d^2 /. {a -> 2 m*p + 2 n*p + n*q,
- b -> 2 m*p + 2 m*q + n*q, c -> 2 m*p + m*q + n*p,
- d -> m*q + n*p + n*q} // FullSimplify
- a^2 + b^2 - 2 c^2 - 2 d^2 /. {a -> m*p + m*q - n*p + n*q,
- b -> m*p - m*q + n*p + n*q, c -> m*p - n*q,
- d -> m*q + n*p} // FullSimplify
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