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Консультация № 190484
26.01.2017, 12:03
0.00 руб.
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
В первый раз знаменатель положительной дроби увеличили на 3, а во второй раз уменьшили на 5. Сумма полученных таким образом дробей оказалась равной 2/3. Найдите знаменатель дроби, если её числитель равен 2.
В первый раз знаменатель положительной дроби увеличили на 3, а во второй раз уменьшили на 5. Сумма полученных таким образом дробей оказалась равной 2/3. Найдите знаменатель дроби, если её числитель равен 2.
Обсуждение
26.01.2017, 14:23
общий
это ответ
Здравствуйте, svrvsvrv!
Обозначим знаменатель дроби через х, тогда дробь имеет вид 2/х
Тогда, по условию, 2/(х+3) + 2/(х-5) = 2/3
Упростив уравнение, получим х2-8х-9=0
Корни уравнения: x1 = -1, x2 = 9
Из условия положительности дроби корень x1 = -1 отпадает.
Остается x2 = 9
Получаем исходную дробь 2/9
Обозначим знаменатель дроби через х, тогда дробь имеет вид 2/х
Тогда, по условию, 2/(х+3) + 2/(х-5) = 2/3
Упростив уравнение, получим х2-8х-9=0
Корни уравнения: x1 = -1, x2 = 9
Из условия положительности дроби корень x1 = -1 отпадает.
Остается x2 = 9
Получаем исходную дробь 2/9
5
Огромное спасибо. Ваше объяснение очень простое, логичное и доступное.
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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