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Консультация № 189759
10.09.2016, 21:52
0.00 руб.
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Здравствуйте! Прошу помощи в следующей задачи ( № 7 ):
Прикрепленные файлы:
Обсуждение
12.09.2016, 10:26
общий
это ответ
Здравствуйте, anton74551!
а) Согласно одному из следствий теоремы Безу, число
является корнем многочлена 
степени не ниже первой тогда и только тогда , когда делится на 
Поэтому поскольку 
постольку - корень многочлена 
и делится на Выполнив, например, деление в столбик, получим, что 
а) Согласно одному из следствий теоремы Безу, число
является корнем многочлена степени не ниже первой тогда и только тогда , когда делится на Поэтому поскольку постольку - корень многочлена и делится на Выполнив, например, деление в столбик, получим, что
Об авторе:
Facta loquuntur.
Facta loquuntur.
12.09.2016, 13:52
общий
это ответ
Здравствуйте, anton74551!
б) В формуле
xn - an = (x - a)(xn + a xn-1 + a2xn-2 + ... + an-1x + an).
доказанной согласно п. а) этой задачи, будем считать n нечетным, n = 2k - 1, и сделаем замену a [$8594$] -a.
Получим:
xn + an = (x + a)(xn - a xn-1 + a2xn-2 - ... + an-1x - an).
Во второй скобке знаки "минус" стоят перед членами с нечетной степенью a.
б) В формуле
xn - an = (x - a)(xn + a xn-1 + a2xn-2 + ... + an-1x + an).
доказанной согласно п. а) этой задачи, будем считать n нечетным, n = 2k - 1, и сделаем замену a [$8594$] -a.
Получим:
xn + an = (x + a)(xn - a xn-1 + a2xn-2 - ... + an-1x - an).
Во второй скобке знаки "минус" стоят перед членами с нечетной степенью a.
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