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