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Консультация № 52028
13.08.2006, 20:33
0.00 руб.
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3
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Здравствуйте!
могут ли быть тождественны следующие ур-ния ( и как из первого получить второе): x^2-2*c*x-2*c*h=0 и x=c+sqrt(c^2+2*c*h) ?thanks!
могут ли быть тождественны следующие ур-ния ( и как из первого получить второе): x^2-2*c*x-2*c*h=0 и x=c+sqrt(c^2+2*c*h) ?thanks!
Обсуждение
Неизвестный
13.08.2006, 21:08
общий
это ответ
Здравствуйте, Sage!
Да они могут быть тождествеными преобразуем второе ур-ния
(x-c)^2=c^2+2*c*h
x^2-2*x*c+c^2-c^2-2*c*h=0
x^2-2*x*c-2*c*h=0
мы получили первое уравнение следовательно, что бы из первого получить второе
нужно к первому прибавить и вычесть с^2
x^2-2*c*x-2*c*h+с^2-с^2=0
Да они могут быть тождествеными преобразуем второе ур-ния
(x-c)^2=c^2+2*c*h
x^2-2*x*c+c^2-c^2-2*c*h=0
x^2-2*x*c-2*c*h=0
мы получили первое уравнение следовательно, что бы из первого получить второе
нужно к первому прибавить и вычесть с^2
x^2-2*c*x-2*c*h+с^2-с^2=0
Неизвестный
13.08.2006, 22:21
общий
это ответ
Здравствуйте, Sage!
Два данных уравнения x^2-2*c*x-2*c*h=0 и x=c+sqrt(c^2+2*c*h) не являютя тождественными, а именно: из первого уравнения получаются два решения
(x-c)^2=c^2+2*c*h =>
1. x-c=sqrt(c^2+2*c*h) =>x=c+sqrt(c^2+2*c*h)
2. x-c=-sqrt(c^2+2*c*h) =>x=c-sqrt(c^2+2*c*h)
Удачи!
Два данных уравнения x^2-2*c*x-2*c*h=0 и x=c+sqrt(c^2+2*c*h) не являютя тождественными, а именно: из первого уравнения получаются два решения
(x-c)^2=c^2+2*c*h =>
1. x-c=sqrt(c^2+2*c*h) =>x=c+sqrt(c^2+2*c*h)
2. x-c=-sqrt(c^2+2*c*h) =>x=c-sqrt(c^2+2*c*h)
Удачи!
Неизвестный
14.08.2006, 12:51
общий
Второе выражение является корнем первого уравнения относительно x. Соответственно, второй корень вычисляется по формуле: x = c-sqrt(c^2+2ch).Для того, чтобы два уравнения были тождественны, нужно, чтобы у первого уравнения было не больше одного корня.Т.е. D=c^2+2ch<=0c*(c+2h) <=0c1=0; c2=-2hТ.о., два уравнения тождественны в том случае, когда:Если h>0 => c принадлежит промежутку [-2h;0]Если h<0 => c принадлежит промежутку [0;-2h]
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