\[\begin{array}{l} {\text{Пусть }}{x_1} + {x_2} + ... + {x_n} = 3,{\text{ }}{y_1} + {y_2} + ... + {y_n} = 4{\text{ и }}{z_1} + {z_2} + ... + {z_n} = 5. \hfill \\ {\text{Доказать}}{\text{, что }}\sqrt {x_1^2 + y_1^2 + z_1^2} + \sqrt {x_2^2 + y_2^2 + z_2^2} + ... + \sqrt {x_n^2 + y_n^2 + z_n^2} \geqslant 5\sqrt 2 . \hfill \\ \end{array}\]