Question

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

Answer 1

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

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