6-6сos²x+7cosx-7=0
cosx=a
6a²-7a+1=0
D=49-24=25
a1=(7-5)/12=1/6⇒cosx=1/6⇒x=+-arccos1/6+2πn,n∈z
x1=-2π+arccos1/6∈[-3π;-π]
x2=-2π-acrcos1/6∈[-3π;-π]
a2=(7+5)/12=1⇒cosx=1⇒x=2πk,k∈z
x3=-2π∈[-3π;-π]
27^4 -9^5=3^(3*4) -3^(2*5)=3^12 -3^10=3^10*(3^2 -1)=3^10 *8 - кратно 8
Обозначим члены геометрической прогрессии через : a ; b ; 36 .
Тогда по свойству геометрической прогрессии : b² = 36a .
Члены арифметической прогрессии : a ; b , 27 , значит : b = (a + 27)/2 .
или 2b = a + 27 .
![\left \{ {{b^{2}=36a } \atop {a=2b-27}} \right.\\\\\left \{ {{b^{2}=36*(2b-27) } \atop {a=2b-27}} \right.\\\\\left \{ {{b^{2}-72b+972=0 } \atop {a=2b-27}} \right.\\\\b^{2}-72b+972=0\\\\D=(-72)^{2}-4*972=5184-3888=1296=36^{2}\\\\b_{1}=\frac{72-36}{2} =18\\\\b_{2}=\frac{72+36}{2}=54\\\\a_{1}=2*18-27=9\\\\a_{2} =2*54-27=81](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bb%5E%7B2%7D%3D36a%20%7D%20%5Catop%20%7Ba%3D2b-27%7D%7D%20%5Cright.%5C%5C%5C%5C%5Cleft%20%5C%7B%20%7B%7Bb%5E%7B2%7D%3D36%2A%282b-27%29%20%7D%20%5Catop%20%7Ba%3D2b-27%7D%7D%20%5Cright.%5C%5C%5C%5C%5Cleft%20%5C%7B%20%7B%7Bb%5E%7B2%7D-72b%2B972%3D0%20%7D%20%5Catop%20%7Ba%3D2b-27%7D%7D%20%5Cright.%5C%5C%5C%5Cb%5E%7B2%7D-72b%2B972%3D0%5C%5C%5C%5CD%3D%28-72%29%5E%7B2%7D-4%2A972%3D5184-3888%3D1296%3D36%5E%7B2%7D%5C%5C%5C%5Cb_%7B1%7D%3D%5Cfrac%7B72-36%7D%7B2%7D%20%3D18%5C%5C%5C%5Cb_%7B2%7D%3D%5Cfrac%7B72%2B36%7D%7B2%7D%3D54%5C%5C%5C%5Ca_%7B1%7D%3D2%2A18-27%3D9%5C%5C%5C%5Ca_%7B2%7D%20%3D2%2A54-27%3D81)
Получили две прогрессии :
9 ; 18 ; 36
81 ; 54 ; 36
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