помогите с номером 13. Created by Mankeysy. algebra-ru

помогите с номером 13...

volkodav575

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Решение во вложении, надеюсь понятно

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Universalka

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2 - 5Cosx - Cos2x = 0
2 - 5Cosx - (2Cos²x - 1)= 0
2 - 5Cosx - 2Cos2x + 1 = 0
2Cos²x + 5Cosx - 3 = 0
Обозначим Cosx = a, где - 1≤ a ≤ 1
2a² +5a - 3 = 0
D = 5² - 4*2*(-3) = 25+24 = 49
a₁ =(- 5 + √49)/4 =(-5 + 7)/4 = 1/2
a₂ = (-5 - 7)/4 = - 3 - не подходит
Cosx = 1/2
x = + - arcCos1/2 + 2πn, n ∈ z
x = + - π/3 + 2πn, n ∈ z
Корни из заданного промежутка: - 5π/3 ; - 7π/3

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