Ответ:3π/2+3πn,n∈z
Объяснение: cosx/3·cos2x/3+sin2x/3·sinx/3-1/2cosx/3=0
cos(2x/3-x/3)-1/2cosx/3=0
cosx/3-1/2cosx/3=0
1/2c0sx/3=0
cosx/3=0
x/3=π/2+πn,n∈z⇒ x=3π/2+3πn,n∈z
(у тебя неточное условие,обрати внимание где знак =?)
(192)^1/2/(3)^1/2=(192:3)^1/2=(64)^1/2=8.Ответ: 8.
1) =х√36х^6= x*I6x³I =x*-6x=-6x². где х<0
2) =2m³ √(9n²/m²)= 2m²* I 3n/m I= 2m²*(-2n/m)=-4mn. где n<0
I I это модуль
![\displaystyle f(x)=x+2\cos x\\\\f'(x)=1-2\sin x=0\\\\2\sin x=1\\\\\sin x=\frac{1}2\\\\\left[\begin{array}{ccc}\displaystyle x=\frac{\pi}{6}+2\pi n;\quad n\in Z\\\\\displaystyle x=\frac{5\pi}6+2\pi n;\quad n \in Z\end{array}\right \\\\\\\underline{...\quad-\quad\quad\frac{\pi}6\quad\quad+\quad\quad\frac{5\pi}6\quad\quad-\quad\quad\frac{13\pi}6\quad\quad+\quad\quad\frac{17\pi}6\quad\quad-\quad...}](https://tex.z-dn.net/?f=%5Cdisplaystyle+f%28x%29%3Dx%2B2%5Ccos+x%5C%5C%5C%5Cf%27%28x%29%3D1-2%5Csin+x%3D0%5C%5C%5C%5C2%5Csin+x%3D1%5C%5C%5C%5C%5Csin+x%3D%5Cfrac%7B1%7D2%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cdisplaystyle+x%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%2B2%5Cpi+n%3B%5Cquad+n%5Cin+Z%5C%5C%5C%5C%5Cdisplaystyle+x%3D%5Cfrac%7B5%5Cpi%7D6%2B2%5Cpi+n%3B%5Cquad+n+%5Cin+Z%5Cend%7Barray%7D%5Cright+%5C%5C%5C%5C%5C%5C%5Cunderline%7B...%5Cquad-%5Cquad%5Cquad%5Cfrac%7B%5Cpi%7D6%5Cquad%5Cquad%2B%5Cquad%5Cquad%5Cfrac%7B5%5Cpi%7D6%5Cquad%5Cquad-%5Cquad%5Cquad%5Cfrac%7B13%5Cpi%7D6%5Cquad%5Cquad%2B%5Cquad%5Cquad%5Cfrac%7B17%5Cpi%7D6%5Cquad%5Cquad-%5Cquad...%7D)
Точки минимума (знак меняется с - на +): ![\displaystyle \boxed{x=\frac{\pi}6+2\pi n;\quad n\in Z}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cboxed%7Bx%3D%5Cfrac%7B%5Cpi%7D6%2B2%5Cpi+n%3B%5Cquad+n%5Cin+Z%7D)
Точки максимума (знак меняется с + на -): ![\displaystyle \boxed{x=\frac{5\pi}6+2\pi n;\quad n\in Z}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cboxed%7Bx%3D%5Cfrac%7B5%5Cpi%7D6%2B2%5Cpi+n%3B%5Cquad+n%5Cin+Z%7D)
![\tt 2\sin^2x-3\sin x\cos x+4\cos^2x=4\\ 2\sin^2x-3\sin x\cos x+4\cos^2x=4(\cos^2x+\sin^2x)\\ 2\sin^2x-3\sin x\cos x+4\cos^2x=4\cos^2x+4\sin^2x\\ 2\sin^2x+3\sin x\cos x=0\\ \sin x(2\sin x+3\cos x)=0](https://tex.z-dn.net/?f=+%5Ctt+2%5Csin%5E2x-3%5Csin+x%5Ccos+x%2B4%5Ccos%5E2x%3D4%5C%5C+2%5Csin%5E2x-3%5Csin+x%5Ccos+x%2B4%5Ccos%5E2x%3D4%28%5Ccos%5E2x%2B%5Csin%5E2x%29%5C%5C+2%5Csin%5E2x-3%5Csin+x%5Ccos+x%2B4%5Ccos%5E2x%3D4%5Ccos%5E2x%2B4%5Csin%5E2x%5C%5C++2%5Csin%5E2x%2B3%5Csin+x%5Ccos+x%3D0%5C%5C+%5Csin+x%282%5Csin+x%2B3%5Ccos+x%29%3D0+)
Произведение равно нулю, если хотя бы один из множителей равен нулю
![\tt \sin x=0~~~\Rightarrow~~~ \boxed{\tt x=\pi k,k \in \mathbb{Z}}](https://tex.z-dn.net/?f=+%5Ctt+%5Csin+x%3D0~~~%5CRightarrow~~~+%5Cboxed%7B%5Ctt+x%3D%5Cpi+k%2Ck+%5Cin+%5Cmathbb%7BZ%7D%7D+)
![\tt 2\sin x+3\cos x=0](https://tex.z-dn.net/?f=+%5Ctt+2%5Csin+x%2B3%5Ccos+x%3D0+)
Разделим левую и правую части уравнения на
, получим:
![\tt 2tgx+3=0\\ tgx=-\frac{3}{2} ~~~\Rightarrow~~~ \boxed{\tt x=-arctg\frac{3}{2} +\pi n,n \in \mathbb{Z}}](https://tex.z-dn.net/?f=+%5Ctt+2tgx%2B3%3D0%5C%5C+tgx%3D-%5Cfrac%7B3%7D%7B2%7D+~~~%5CRightarrow~~~+%5Cboxed%7B%5Ctt+x%3D-arctg%5Cfrac%7B3%7D%7B2%7D+%2B%5Cpi+n%2Cn+%5Cin+%5Cmathbb%7BZ%7D%7D++)