\[\boxed{\text{754.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[Пусть\ x_{1},\ x_{2},\ x_{3} - три\ \]
\[последовательных\ \]
\[четных\ числа.\]
\[x_{1}^{2} + x_{2}^{2} = x_{3}^{2}\]
\[x_{2} = x_{1} + 2,\ x_{3} = x_{1} + 4.\]
\[Составим\ уравнение:\ \]
\[x_{1}^{2} + \left( x_{1} + 2 \right)^{2} = \left( x_{1} + 4 \right)^{2}\]
\[x_{1}^{2} + x_{1}^{2} + 4x_{1} + 4 =\]
\[= x_{1}^{2} + 8x_{1} + 16\]
\[x_{1}^{2} - 4x_{1} - 12 = 0\]
\[D = 16 + 48 = 64\]
\[x_{1,2} = \frac{4 \pm 8}{2} = 6;\ - 2\]
\[то\ есть:\]
\[x_{1} = 6,\ x_{2} = 8,\ x_{3} = 10\ \ или\]
\[x_{1} = - 2,\ x_{2} = 0,\ x_{3} = 2.\ \]
\[Ответ:6,\ 8,\ 10\ или\ ( - 2),\ 0,\ 2.\]