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Консультация № 197001
07.11.2019, 13:22
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Здравствуйте! Уважаемые эксперты, нужно срочно решить следующие задания. Заранее благодарен за ответ.
Найдите все целочисленные решения уравнения:
а) 2x^2=2y^2+3xy+7
б) (x^2+y^2)*(x+y-3)=2xy
Найдите все целочисленные решения уравнения:
а) 2x^2=2y^2+3xy+7
б) (x^2+y^2)*(x+y-3)=2xy
Обсуждение
12.08.2022, 13:57
общий
это ответ
Здравствуйте, kandALS!
Рассмотрим уравнение а:
Если
-- целые числа, то сомножители в левой части последнего уравнения тоже должны быть целыми числами. При этом возможны четыре случая:
1)
2)
3)
4)
Во всех случаях
и 
не являются целыми числами. Значит, у рассмотренного уравнения нет целочисленных решений.
Рассмотрим уравнение а:
Если
-- целые числа, то сомножители в левой части последнего уравнения тоже должны быть целыми числами. При этом возможны четыре случая:1)
2)
3)
4)
Во всех случаях
и не являются целыми числами. Значит, у рассмотренного уравнения нет целочисленных решений.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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