\(x^{672}+y^{672}\) = 6,912 và \(x^{1344}+y^{1344}\) = 33,76244
Ta có:
\(x^{672}+y^{672}=6,912\)
\(\Leftrightarrow\left(x^{672}+y^{672}\right)^2=6,912^2\)
\(\Leftrightarrow x^{1344}+y^{1344}+2x^{672}y^{672}=6,912^2\)
\(\Leftrightarrow33,76244+2x^{672}y^{672}=6,912^2\)
\(\Leftrightarrow x^{672}y^{672}=7,006652\)
Ta có:
\(\left\{{}\begin{matrix}x^{672}+y^{672}=6,912\\x^{1344}+y^{1344}=33,76244\end{matrix}\right.\)
\(\Rightarrow\left(x^{672}+y^{672}\right)\left(x^{1344}+y^{1344}\right)=6,912.33,76244\)
\(\Leftrightarrow x^{2016}+y^{2016}+x^{672}y^{1344}+y^{672}x^{1344}=233,36598528\)
\(\Leftrightarrow x^{2016}+y^{2016}+x^{672}y^{672}\left(x^{672}+y^{672}\right)=233,36598528\)
\(\Leftrightarrow x^{2016}+y^{2016}+48,429978624=233,36598528\)
\(\Leftrightarrow x^{2016}+y^{2016}=184,936006656\)
