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Консультация № 197202
25.11.2019, 19:57
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Найдите число целых решений неравенства
(x^2-8x+16)/((x-4)*(x-6))≥-1, принадлежащих отрезку [3;7]
Найдите число целых решений неравенства
(x^2-8x+16)/((x-4)*(x-6))≥-1, принадлежащих отрезку [3;7]
Обсуждение
26.11.2019, 00:33
общий
это ответ
Здравствуйте, zhaizhbekowa!
Область определения данного неравенства: х [$8800$] 4 и х [$8800$] 6
Умножив обе части неравенства на знаменатель, раскрыв скобки, приведя подобные, сократив, получим:
x2 - 9x + 20x [$8805$] 0
Если приравняем левую часть к нулю, то получим
квадратное уравнение с корнями х = 4 и х = 5
Тогда решением неравенства будет x [$8712$] (-[$8734$], 4] [$8746$] [5, +[$8734$]).
Целыми решениями на интервале [3, 7] будут 3, 4, 5, 6, 7
Но, с учётом области определения, остаются 3, 5, 7
Т.о. число целых решений будет равно 3
Область определения данного неравенства: х [$8800$] 4 и х [$8800$] 6
Умножив обе части неравенства на знаменатель, раскрыв скобки, приведя подобные, сократив, получим:
x2 - 9x + 20x [$8805$] 0
Если приравняем левую часть к нулю, то получим
квадратное уравнение с корнями х = 4 и х = 5
Тогда решением неравенства будет x [$8712$] (-[$8734$], 4] [$8746$] [5, +[$8734$]).
Целыми решениями на интервале [3, 7] будут 3, 4, 5, 6, 7
Но, с учётом области определения, остаются 3, 5, 7
Т.о. число целых решений будет равно 3
5
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
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