\(c,\left(x-9\right)^2+x^2-81=0\)
\(\Leftrightarrow\left(x-9\right)\left(x-9\right)+\left(x-9\right)\left(x+9\right)=0\)
\(\Leftrightarrow\left(x-9\right)\left(x-9+x+9\right)=0\)
\(\Leftrightarrow2x\left(x-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=0\\x-9=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=9\end{matrix}\right.\)
\(\left(x-9\right)^2+x^2-81=0\)
\(\Leftrightarrow\left(x-9\right)^2+x^2-9^2=0\)
\(\Leftrightarrow\left(x-9\right)^2+\left(x-9\right)\left(x+9\right)=0\)
\(\Leftrightarrow\left(x-9\right)\left[\left(x-9\right)+\left(x+9\right)\right]=0\)
\(\Leftrightarrow\left(x-9\right)\left(x-9+x+9\right)=0\)
\(\Leftrightarrow\left(x-9\right)\left(2x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-9=0\\2x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=9\\x=0\end{matrix}\right.\)
\(\left(x-9\right)^2+x^2-81=0\)
\(\Leftrightarrow\left(x-9\right)^2+\left(x^2-81\right)=0\)
\(\Leftrightarrow\left(x-9\right)^2+\left(x-9\right)\left(x+9\right)=0\)
\(\Leftrightarrow\left(x-9\right)\left(x-9+x+9\right)=0\)
\(\Leftrightarrow\left(x-9\right)2x=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-9=0\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9\\x=0\end{matrix}\right.\)
\(\text{Vậy phương trình có tập nghiệm là }S=\left\{0;9\right\}\)
