Log^2 (2) (cos^2x)-22log2(cosx)-12=0 решить

Question

Log^2 (2) (cos^2x)-22log2(cosx)-12=0 решить

Answer 1

Log^2 cos^2x - 22 log cos x - 12 = 0 | cos x > 0
log^2 cos^2x - 11 log cos^2 x - 12 = 0
log cos^2 x = t, t <= 0 (cos^2 x <= 1)<br>t^2 - 11 t - 12 = 0
(t + 1)(t - 12) = 0
t = -1
log cos^2 x = -1
cos^2 x = 1/2
cos x = + 1/sqrt(2) | ( cos x > 0 )
x = +- П/4 + 2Пk, k = ..., -1, 0, 1, ...

Comments

А как получилось 11?

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2 log(x) = log(x^2)

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И cos=1/2 разве не пи\3?

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Там cos^2 x = 1/2. Соответственно, cos x = +- sqrt(1/2)