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qwerty91a
@qwerty91a
July 2022
1
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ДАЮ 50 БАЛЛОВ!!!
Найдите произведение корней уравнения
x^(lgx)=1000x^2
Как можно подробно плз
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IrkaShevko
Verified answer
Прологарифмируем обе части по основанию 10:
lg (x^(lgx)) = lg (10^3 * x^2)
(lgx)^2 = 3 + 2lgx
lgx = y
y^2 - 2y - 3 = 0
D = 4 + 12 = 16
y1 = (2 + 4)/2 = 3
lgx = 3
x = 10^3 = 1000
y2 = (2 - 4)/2 = -1
lgx = -1
x = 10^(-1) = 0,1
x1*x2 = 100
Ответ: 100
1 votes
Thanks 3
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Answers & Comments
Verified answer
Прологарифмируем обе части по основанию 10:lg (x^(lgx)) = lg (10^3 * x^2)
(lgx)^2 = 3 + 2lgx
lgx = y
y^2 - 2y - 3 = 0
D = 4 + 12 = 16
y1 = (2 + 4)/2 = 3
lgx = 3
x = 10^3 = 1000
y2 = (2 - 4)/2 = -1
lgx = -1
x = 10^(-1) = 0,1
x1*x2 = 100
Ответ: 100