Решите уравнение:
[tex] \frac{2cosx + 1}{ \sqrt{27 - 6x - x^{2} } } = 0 [/tex]
[tex] \frac{2cosx + 1}{ \sqrt{27 - 6x - x^{2} } } = 0 [/tex]
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ОДЗ27-6х-х²>0
x²+6x-27<0
D=36+4*27=144=12²
x₁=(-6+12)/2=3
x₂=(-6-12)/2=-9
(x+9)(x-3)<0
x∈(-9; 3)
Т.к. знаменатель не равен 0, то
2cosx+1=0
2cosx=-1
cosx=-1/2
x=2π/3+2πk, k∈Z
x=4π/3+2πk, k∈Z
x=4π/3+2πk, k∈Z