Выполним задание.
$$ (5+\sqrt{2})^2 + (5-\sqrt{2})^2 = (25 + 10\sqrt{2} + 2) + (25 - 10\sqrt{2} + 2) = 25 + 10\sqrt{2} + 2 + 25 - 10\sqrt{2} + 2 = 25+2+25+2 = 54 $$
Ответ: 54