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Консультация № 187883
16.06.2014, 22:07
340.00 руб.
0
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Помогите выразить через основные симметрические многочлены
F(x1,x2,x3,x4)=(x1x2+x3x4)(x1x3+x2x4)(x1x4+x2x3)
Помогите выразить через основные симметрические многочлены
F(x1,x2,x3,x4)=(x1x2+x3x4)(x1x3+x2x4)(x1x4+x2x3)
Обсуждение
18.06.2014, 11:16
общий
это ответ
Здравствуйте, Katerina!
S1=x1+x2+x3+x4
S2=x1x2+x1x3+x1x4+x2x3+x2x4+x3x4
S3=x1x2x3+x1x2x4+x1x3x4+x2x3x4
S4=x1x2x3x4
S=(x1x2+x3x4)(x1x3+x2x4)(x1x4+x2x3)=
=[x12x22x32+x12x22x42+x12x32x42+x22x32x42]+
+[x13x2x3x4+x1x23x3x4+x1x2x33x4+x1x2x3x43]=
=[S32-2S2S4]+[S12S4-2S2S4]=
=S32+S12S4-4S2S4
S1=x1+x2+x3+x4
S2=x1x2+x1x3+x1x4+x2x3+x2x4+x3x4
S3=x1x2x3+x1x2x4+x1x3x4+x2x3x4
S4=x1x2x3x4
S=(x1x2+x3x4)(x1x3+x2x4)(x1x4+x2x3)=
=[x12x22x32+x12x22x42+x12x32x42+x22x32x42]+
+[x13x2x3x4+x1x23x3x4+x1x2x33x4+x1x2x3x43]=
=[S32-2S2S4]+[S12S4-2S2S4]=
=S32+S12S4-4S2S4
19.06.2014, 00:32
общий
Здравствуйте! Если бы Вы посетили этот ресурс: http://ph4s.ru/book_mat_algebra.html и загрузили книгу Винберг Э.Б. Курс алгебры. 2-е изд. испр. допол.. 2002 год. 544 стр. dgvu. 3.2 Мб, то нашли бы в ней обстоятельные указания к решению задачи. Заодно сохранили бы деньги и научились решать подобные задачи... 
Об авторе:
Facta loquuntur.
Facta loquuntur.
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