Question

помогите!
4^cosx+4^-cosx=52 [-3П ; -3П2]

Answer 1

$4^{cosx}+4^{-cosx}=5/2\\4^{cosx}+ frac{1}{4^{cosx}}=5/2\\t=4^{cosx}\\t+ frac{1}{t}= frac{5}{2}|*2t\\2t^2-5t+2=0\D=(-5)^2-4*2*2=25-16=9=3^2\t_1=(5+3)/4=2\t_2=(5-3)/4=1/2$

$4^{cosx}=2\2^{2cosx}=2^1\2cosx=1\cosx=1/2\x_1=б pi /3+2 pi n, nin Z\\4^{cosx}=1/2\2^{2cosx}=2^{-1}\2cosx=-1\cosx=-1/2\x_2=б2 pi /3+2 pi n, nin Z$

[-3π;-3π/2]
x₁=-3π+π/3=(-9π+π)/3=-8π/3
x₂=-2π-π/3=(-6π-π)/3=-7π/3
x₃=-2π+π/3=(-6π+π)/3=-5π/3