\(x^4-20x^2+100-y^4+28y^2-196=11\)
\(\Leftrightarrow\left(x^2-10\right)^2-\left(y^2-14\right)^2=11\)
\(\Leftrightarrow\left(x^2+y^2-24\right)\left(x^2-y^2+4\right)=11\)
TH1: \(\left\{{}\begin{matrix}x^2+y^2-24=-11\\x^2-y^2+4=-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x^2=4\\y^2=9\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\pm2\\y=\pm3\end{matrix}\right.\)
TH2: \(\left\{{}\begin{matrix}x^2+y^2-24=-1\\x^2-y^2+4=-11\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x^2=4\\y^2=19\end{matrix}\right.\) \(\Rightarrow\) ko có y nguyên (loại)
TH3: \(\left\{{}\begin{matrix}x^2+y^2-24=11\\x^2-y^2+4=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x^2=16\\y^2=19\end{matrix}\right.\) \(\Rightarrow\) ko có y nguyên (loại)
TH4: \(\left\{{}\begin{matrix}x^2+y^2-24=1\\x^2-y^2+4=11\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x^2=16\\y^2=9\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\pm4\\y=\pm3\end{matrix}\right.\)
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