\(\left(x^2+9\right)\left[x^2+9+9\left(y-1\right)\right]=22\left(y-1\right)^2\)
Đặt \(\left\{{}\begin{matrix}x^2+9=a\\y-1=b\end{matrix}\right.\)
\(\Rightarrow a\left(a+9b\right)=22b^2\Leftrightarrow a^2+9ab-22b^2=0\)
\(\Leftrightarrow\left(a-2b\right)\left(a+11b\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}a=2b\\a=-11b\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x^2+9=2\left(y-1\right)\\x^2+9=-11\left(y-1\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2-2=2y-13\\x^2-2=-11y\end{matrix}\right.\) thay xuống dưới:
TH1: \(x^2-2=2y-13\Rightarrow2y-13=4y\sqrt{y+1}\)
Đặt \(\sqrt{y+1}=t\ge0\)
\(\Rightarrow2\left(t^2-1\right)-13=4t\left(t^2-1\right)\)
\(\Leftrightarrow4t^3-2t^2-4t+15=0\) (pt bậc 3 này ko giải được bằng kiến thức phổ thông :) )
TH2: \(x^2-2=-11y\Rightarrow-11y=4y\sqrt{y+1}\)
\(\Rightarrow y=0\Rightarrow x=\pm\sqrt{2}\)
