3cos^2 pi x +4cos pi x-7=o

Question

3cos^2 pi x +4cos pi x-7=o

Answer 1

Cosπx = t
3t² +4t - 7 = 0
D= b² - 4ac = 16 -4*3*(-7) = 100
t1 = (-4+10)/6 = 1
t2 = (-4 -10)/6 = -14/6 = -7/3
a) t = 1
Cosπx = 1
πx = 2πk , k ∈Z
x = 2k, k ∈Z
б) Cosπx = -7/3 (нет решений)
Ответ: х= 2k , k∈Z