3 - 4sin²(3x + π/3) = 0
3 = 4sin²(3x + π/3)
sin²(3x + π/3) = 3/4
sin(3x + π/3) = ±√3/2
1) sin(3x + π/3) = √3/2
3x + π/3 = (-1)ⁿπ/3 + πn, n ∈ Z
x = (-1)ⁿπ/9 - π/9 + πn/3, n ∈ Z
2) sin(3x + π/3) = -√3/2
3x + π/3 = (-1)ⁿ+¹π/3 + πn, n ∈ Z
x = (-1)ⁿ+¹π/9 - π/9 + πn/3, n ∈ Z
Смотри решение во вложении
В
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N-ый член арифметической прогрессии вычисляется по формуле:
![a_n=a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d)
Пользуясь этой формулой, мы будем получать
![a_{10}+a_8=a_1+9d+a_1+7d=2a_1+16d=\frac{3}{4}](https://tex.z-dn.net/?f=a_%7B10%7D%2Ba_8%3Da_1%2B9d%2Ba_1%2B7d%3D2a_1%2B16d%3D%5Cfrac%7B3%7D%7B4%7D)
Окончательно имеем
![a_5+a_{13}=a_1+4d+a_1+12d=2a_1+16d= \frac{3}{4}](https://tex.z-dn.net/?f=a_5%2Ba_%7B13%7D%3Da_1%2B4d%2Ba_1%2B12d%3D2a_1%2B16d%3D+%5Cfrac%7B3%7D%7B4%7D+)
Ответ:
![a_5+a_{13}= \frac{3}{4}](https://tex.z-dn.net/?f=a_5%2Ba_%7B13%7D%3D+%5Cfrac%7B3%7D%7B4%7D+)