\begin{equation}
\large
\begin{aligned}
& 设x=AE+AF，y=AE \cdot AF\\
& AB^2=441 \Rightarrow AB=21\\
& S(AEF)= \frac{AE \cdot BC}{2}+ \frac{AF \cdot CD}{2}= \frac{(AE+AF) \cdot AB}{2}= \frac{21x}{2}\\
& S(AEF)=\frac{AE \cdot AF}{2}=\frac{y}{2}=\frac{21x}{2} \Rightarrow y=21x\\
&  \\
&  \\
& 设EF边的高为AK，m=EF，n=AK\\
& GH^2=440 \Rightarrow GH=\sqrt{440}\\
& S(AEF)= \frac{EJ \cdot GJ}{2}+ \frac{IJ \cdot GJ}{2}+ \frac{FI \cdot HI}{2}+S(AGIH)= \frac{EF \cdot GH}{2}+\frac{AK \cdot GH}{2}= \frac{(m+n) \cdot \sqrt{440}}{2}\\
& S(AEF)=\frac{EF \cdot AK}{2}=\frac{m \cdot n}{2}= \frac{21x}{2} \Rightarrow n=\frac{21x}{m}\\
&  \\
&  \\
& m^2=AE^2+AF^2=x^2-2y=x^2-42x\\
& S(AEF)= \frac{21x}{2}=\frac{(m+n) \cdot \sqrt{440}}{2}\\
& \Rightarrow x^2 \cdot 441=(m^2+2m \cdot n+n^2) \cdot 440=(m^2+42x+\frac{441 \cdot x^2}{m^2}) \cdot 440=(x^2-42x+42x+\frac{441 \cdot x^2}{x^2-42x}) \cdot 440\\
& \Rightarrow x^2-42x-440 \cdot 441=0 \Rightarrow x=462\\
\end{aligned}
\end{equation}

【 在 mvtec 的大作中提到: 】
: tk-eculid
: 简直就是
: 神器
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修改:lcvd FROM 222.129.54.*
FROM 222.129.54.*