![\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)
0,7х-2,1=0,5х+0,5
0,7х-0,5х=0,5+2,1
0,2х=2,6
Х=13
Sкв=36+12=48
Sкв=a^2 где а сторона квадрата
48=a^2
a=4√3
1
{x+y=-2 ⇒x=-y-2
{y^2-3x=6
y²+3y+6-6=0
y²+3y=0
y(y+3)=0
y=0⇒x=-2
y=-3⇒x=1
(-2;0);(1;-3)
2
{x^2+y^2=17
{y-x=3⇒y=3+x
x²+9+6x+x²-17=0
2x²+6x-8=0
x²+3x-4=0
x1+x2=-3 U x1*x2=-4
x1=-4⇒y1=-1
x2=1⇒y2=4
(-4;-1);(1;4)
3
{x-y=1 ⇒x=1+y
{x-4y^2=1
1+y-4y²-1=0
y-4y²=0
y(1-4y)=0
y=0⇒x=1
y=1/4⇒x=1 1/4
(1;0);(1 1/4;1/4)
4
{x+2y^2=4
{x-y=4
отнимем
2y²+y=0
y(2y+1)=0
y=0⇒x-0=4⇒x=4
y=-0,5⇒x+0,5=4⇒x=3,5
(4;0);(3,5;-0,5)