Question

2cos^2x-3cosx+1=0

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Answer 1

Ответ:

x = ± π/3 + 2πn, n ∈Z

x = 2πk, k ∈Z

Объяснение:

2cos²x - 3cosx + 1 = 0

cosx = t

2t² - 3t + 1 = 0

D = 9 - 8 = 1

t₁ = (3 - 1)/4 = 1/2

t₂ = (3 + 1)/4 = 1

1) cosx = 1/2

x = ± arccos(1/2) + 2πn, n ∈ Z

x = ± π/3 + 2πn, n ∈Z

2) cosx = 1

x = 2πk, k ∈Z