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Консультация № 44656
30.05.2006, 10:47
0.00 руб.
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1
1
Здравствуйте!
Вопросы, конечно, не серьёзный. А всё-таки:
1. Как внести множитель под знак корня в дроби?
2. Объясните пожалуйста: освободится от иррациональности в числителе (в знаменателе)?
С уважением!
Вопросы, конечно, не серьёзный. А всё-таки:
1. Как внести множитель под знак корня в дроби?
2. Объясните пожалуйста: освободится от иррациональности в числителе (в знаменателе)?
С уважением!
Обсуждение
Неизвестный
30.05.2006, 17:09
общий
это ответ
Здравствуйте, Aslan!
1. a*b^1/n=(a^n*b)^1/n
Множитель возводится в степень корня
2. Нужно домножить и числитель, и знаменатель на сопряженное выражение. Тогда после раскрытия скобок получится выражение без иррациональности. Работает только для алгебраических чисел, т.е. чисел, которые являются корнями уравнений с рациональными коэффициентами. Например, если есть желание избавиться от числа pi или e, то это не получится, т.к. они являются не алгебраическими, а трансцендентными числами.
Пример:
1/(2-sqrt(3)=(2+sqrt(3))/((2-sqrt(3))*(2+sqrt(3)))=(2+sqrt(3))/(4-(sqrt(3))^2)=(2+sqrt(3))/(4-3)=2+sqrt(3)
1. a*b^1/n=(a^n*b)^1/n
Множитель возводится в степень корня
2. Нужно домножить и числитель, и знаменатель на сопряженное выражение. Тогда после раскрытия скобок получится выражение без иррациональности. Работает только для алгебраических чисел, т.е. чисел, которые являются корнями уравнений с рациональными коэффициентами. Например, если есть желание избавиться от числа pi или e, то это не получится, т.к. они являются не алгебраическими, а трансцендентными числами.
Пример:
1/(2-sqrt(3)=(2+sqrt(3))/((2-sqrt(3))*(2+sqrt(3)))=(2+sqrt(3))/(4-(sqrt(3))^2)=(2+sqrt(3))/(4-3)=2+sqrt(3)
Форма ответа
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