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Консультация № 110012
18.11.2007, 17:09
0.00 руб.
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Здравствуйте эксперты, помогите с задачкой:
Доказать, что P(x,y)=(x^2007)*(y^2008)+1 , нельзя представить в виде произведения двух функций, одна из которых зависит только от x, а другая только от y.
Доказать, что P(x,y)=(x^2007)*(y^2008)+1 , нельзя представить в виде произведения двух функций, одна из которых зависит только от x, а другая только от y.
Обсуждение
Неизвестный
19.11.2007, 09:27
общий
это ответ
Здравствуйте, Tribak!
Доказать, что P(x,y)=x<sup>2007</sup>y<sup>2008</sup>+1 , нельзя представить в виде произведения двух функций, одна из которых зависит только от x, а другая только от y.</body>
Доказательство от обратного. Предположим, что можно и P(x,y) = f(x)g(y)
При x = 0 P(x,y) = 1 при всех y. Тогда f(0)g(y) = 1 или g(y) = 1/f(0), т.е. g(y) = const.
Аналогично для y = 0 P(x,y) = 1 при всех x и f(x) = 1/g(0), т.е. f(x) = const.
Тогда P(x,y) = f(x)g(y) = 1 при всех x и y, что неверно.
Доказать, что P(x,y)=x<sup>2007</sup>y<sup>2008</sup>+1 , нельзя представить в виде произведения двух функций, одна из которых зависит только от x, а другая только от y.</body>
Доказательство от обратного. Предположим, что можно и P(x,y) = f(x)g(y)
При x = 0 P(x,y) = 1 при всех y. Тогда f(0)g(y) = 1 или g(y) = 1/f(0), т.е. g(y) = const.
Аналогично для y = 0 P(x,y) = 1 при всех x и f(x) = 1/g(0), т.е. f(x) = const.
Тогда P(x,y) = f(x)g(y) = 1 при всех x и y, что неверно.
Форма ответа
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