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sabinaimirsy
@sabinaimirsy
July 2022
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Segrif
9 * 3^2cos(x) = 3 * 3^2(cos(x) + 1/2)
10sqrt(3) * 3^cos(x) = 10 * 3^(cos(x) + 1/2)
3^(cos(x) + 1/2) = z -->
3z^2 - 10z + 3 = 0
z^2 - 10/3 z + 1 = 0
(z - 3)(z - 1/3) = 0
1. z = 1/3 --> 3^(cos(x) + 1/2) = 3^(-1) --> cos(x) + 1/2 = -1 - нет решений, т.к. |cos(x)| <= 1
2. z = 3 --> 3^(cos(x) + 1/2) = 3^1 --> cos(x) + 1/2 = 1
cos(x) = 1/2
x = +- П/3 + 2Пk, k = ..., -1, 0, 1, ...
На отрезке [3П/2, 4П]: x = 5П/3, 7П/3, 11П/3
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Answers & Comments
10sqrt(3) * 3^cos(x) = 10 * 3^(cos(x) + 1/2)
3^(cos(x) + 1/2) = z -->
3z^2 - 10z + 3 = 0
z^2 - 10/3 z + 1 = 0
(z - 3)(z - 1/3) = 0
1. z = 1/3 --> 3^(cos(x) + 1/2) = 3^(-1) --> cos(x) + 1/2 = -1 - нет решений, т.к. |cos(x)| <= 1
2. z = 3 --> 3^(cos(x) + 1/2) = 3^1 --> cos(x) + 1/2 = 1
cos(x) = 1/2
x = +- П/3 + 2Пk, k = ..., -1, 0, 1, ...
На отрезке [3П/2, 4П]: x = 5П/3, 7П/3, 11П/3