x2 + y2 + 153 = 6 ( x + 4y )
⇔ x2 + y2 - 6x - 24y + 153 = 0
⇔ x2 - 6x + 9 + y2 - 24y + 144 = 0
⇔ ( x - 3 )2 + ( y - 12 )2 = 0
\(\Leftrightarrow\left\{{}\begin{matrix}x-3=0\\y-12=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=12\end{matrix}\right.\)
⇒ x + y = 15