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Консультация № 199093
23.08.2020, 20:41
0.00 руб.
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3
1
Здравствуйте! Прошу помощи в следующем вопросе:
Необходимо найти число целых решений неравенства. Само неравенство будет ниже.
-((1)\(x+1)) ≥ ((x^2 - 3x -2)\ (x+1)(x+3))
Необходимо найти число целых решений неравенства. Само неравенство будет ниже.
-((1)\(x+1)) ≥ ((x^2 - 3x -2)\ (x+1)(x+3))
Обсуждение
23.08.2020, 21:43
общий
это ответ
Здравствуйте, Алексей_Pb!
Найдем корни числителя и знаменателя:
Нанесём полученные корни на числовую ось: корни числителя отметим заштрихованными точками (неравенство нестрогое (
)), а коорни знаменателя - выколотыми точками (знаменатель дроби не должен быть равен 0)
Определим знак на крайнем правом промежутке: коэффициенты при
в числителе и при 
в каждой скобке в знаменателе проложительны, поэтому знак на крайнем правом промежутке +
При переходе через корень нечётной кратности, то знак меняется на противоположный, если корень чётной кратности, то знак не меняется
Выбираем промежутки со знаком "-", так как знак неравенства
Решение неравенства:
Целые решения неравенства:
и 
, то есть неравенство имеет 
целых решения
Ответ:
Найдем корни числителя и знаменателя:
Нанесём полученные корни на числовую ось: корни числителя отметим заштрихованными точками (неравенство нестрогое (
)), а коорни знаменателя - выколотыми точками (знаменатель дроби не должен быть равен 0)Определим знак на крайнем правом промежутке: коэффициенты при
в числителе и при в каждой скобке в знаменателе проложительны, поэтому знак на крайнем правом промежутке +При переходе через корень нечётной кратности, то знак меняется на противоположный, если корень чётной кратности, то знак не меняется
Выбираем промежутки со знаком "-", так как знак неравенства
Решение неравенства:
Целые решения неравенства:
и , то есть неравенство имеет целых решенияОтвет:
5
Благодарю за помощь!
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