Х - задуманное число
3х+2>2 или 3х>0, х>0
9x-5<13 или 9х<18, х<2
Задумано целое число, а т.к. 0<x<2, то значит задумали число 1
ОДЗ :
x² - 2x - 8 > 0
(x - 4)(x + 2) > 0
+ - +
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- 2 4
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x ∈ ( - ∞ , - 2) ∪ (4 ; + ∞)
![log_{\frac{1}{3} }(x^{2}-2x-8)+3>0\\\\log_{\frac{1}{3} }(x^{2}-2x-8)>-3\\\\x^{2}-2x-8<27\\\\x^{2}-2x-35<0\\\\x^{2}-2x-35=0\\\\D=(-2)^{2}-4*(-35)=4+140=144=12^{2}\\\\x_{1}=\frac{2+12}{2}=7\\\\x_{2}=\frac{2-12}{2} =-5](https://tex.z-dn.net/?f=log_%7B%5Cfrac%7B1%7D%7B3%7D+%7D%28x%5E%7B2%7D-2x-8%29%2B3%3E0%5C%5C%5C%5Clog_%7B%5Cfrac%7B1%7D%7B3%7D+%7D%28x%5E%7B2%7D-2x-8%29%3E-3%5C%5C%5C%5Cx%5E%7B2%7D-2x-8%3C27%5C%5C%5C%5Cx%5E%7B2%7D-2x-35%3C0%5C%5C%5C%5Cx%5E%7B2%7D-2x-35%3D0%5C%5C%5C%5CD%3D%28-2%29%5E%7B2%7D-4%2A%28-35%29%3D4%2B140%3D144%3D12%5E%7B2%7D%5C%5C%5C%5Cx_%7B1%7D%3D%5Cfrac%7B2%2B12%7D%7B2%7D%3D7%5C%5C%5C%5Cx_%7B2%7D%3D%5Cfrac%7B2-12%7D%7B2%7D+%3D-5)
+ - +
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- 5 7
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x ∈ (- 5 , 7)
С учётом ОДЗ окончательный ответ :
x ∈ (- 5 ; - 2) ∪ (4 , 7)
Sint=-1/2
t=(-1)^n*arcsin(-1/2)+pi*n, n<u /><em />∈Z
t=(-1)^n+1*(pi/6)+pi*n, n∈Z.