Svar:
# X = 2npi + - (2pi) / 3 #
Forklaring:
# Rarrcos2x + 5cosx + 3 = 0 #
# rarr2cos ^ 2x-1 + 5cosx + 3 = 0 #
# rarr2cos ^ 2x + 5cosx + 2 = 0 #
# rarr2cos ^ 2x + 4cosx + cosx + 2 = 0 #
# Rarr2cosx (cosx + 2) +1 (cosx + 2) = 0 #
#rarr (2cosx + 1) (cosx + 2) = 0 #
enten, # 2cosx + 1 = 0 #
# Rarrcosx = -1 / 2 = cos ((2pi) / 3) #
# Rarrx = 2npi + - (2pi) / 3 # hvor # NrarrZ #
Eller, # Cosx + 2 = 0 #
# Rarrcosx = -2 # hvilket er uacceptabelt.
Så den generelle løsning er # X = 2npi + - (2pi) / 3 #.
Svar:
# Theta = 2kpi + - (2pi) / 3, Kinz #
Forklaring:
# Cos2theta + 5costheta + 3 = 0 #
#:. 2cos ^ 2-theta-1 + 5costheta + 3 = 0 #
#:. 2cos ^ 2-theta + 5costheta + 2 = 0 #
#:. 2cos ^ 2-theta + 4costheta + costheta + 2 = 0 #
#:. 2costheta (costheta + 2) +1 (costheta + 2) = 0 #
#:. (costheta + 2) (2costheta + 1) = 0 #
# => costheta = -2! i -1,1, eller costheta = -1 / 2 #
# => Costheta = cos (pi-pi / 3) = cos ((2pi) / 3) #
# Theta = 2kpi + - (2pi) / 3, Kinz #
Svar:
Brug # cos2theta = 2 (costheta) ^ 2-1 # og den generelle løsning af #costheta = cosalpha # er # Theta = 2npi + -alfa #; # N Z #
Forklaring:
# Cos2theta + 5costheta + 3 #
# = 2 (costheta) ^ 2-1 + 5costheta + 3 #
# = 2 (costheta) ^ 2 + 5costheta + 2 #
#rArr (costheta + 1/2) (costheta + 2) = 0 #
Her #costheta = -2 # er ikke muligt
Så vi finder kun de generelle løsninger af # Costheta = -1/2 #
# RArrcostheta = (2pi) / 3 #
#:. theta = 2npi + - (2pi) / 3; n Z #
