10 класс, физ-мат. ПОМОГИТЕ ПЛИЗ!! 4^(cos2x) + 4^(cos²x) =3...

Astronavtka @Astronavtka

May 2022 1 15 Report

10 класс, физ-мат. ПОМОГИТЕ ПЛИЗ!!
4^(cos2x) + 4^(cos²x) =3

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Universalka

Verified answer

$4^{Cos2x}+4^{Cos^{2} x} =3\\\\4^{2Cos^{2}x-1 }+4^{Cos^{2}x } =3\\\\\frac{1}{4}* (4^{Cos^{2}x })^{2}+4^{Cos^{2}x }-3=0\\\\4^{Cos^{2}x }=m,m>0\\\\\frac{1}{4} m^{2}+m-3=0|*4\\\\m^{2}+4m-12=0\\\\m_{1}=2\\\\m_{2}=-6$

$Cos^{2}x=\frac{1}{2}\\\\1)Cosx=\frac{\sqrt{2} }{2}\\\\x=\pm\frac{\pi }{4}+2\pi n,n\in z\\\\2)Cosx=-\frac{\sqrt{2} }{2}\\\\x=\pm\frac{3\pi }{4}+2\pi n,n\in z$

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