Question

Cos4x-3cos2x=1 решить уравнение

Answer 1

Решение во вложении.........................................................................................

Answer 2

$Cos4x-3Cos2x=1\\2Cos ^{2} 2x-1-3Cos2x-1=0\\2Cos ^{2}2x-3Cos2x-2=0\\Cos2x=m;-1 leq m leq 1 \\2m ^{2} -3m-2=0\\D=9-4*2*(-2)=9+16=25= 5^{2}\\ m_{1} = frac{3-5}{4}=- frac{1}{2}\\ m_{2}= frac{3+5}{4}=2$
m₂ - не подходит
$Cos2x=- frac{1}{2}\\2x=+- frac{2 pi }{3} +2 pi n\\x=+- frac{ pi }{3}+ pi n,n$∈z