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![2^x+2^{-x+1}-3<0](https://tex.z-dn.net/?f=2%5Ex%2B2%5E%7B-x%2B1%7D-3%3C0)
![2^x+2*\frac{1}{2^x} -3<0](https://tex.z-dn.net/?f=2%5Ex%2B2%2A%5Cfrac%7B1%7D%7B2%5Ex%7D+-3%3C0)
Пусть
, при этом y>0;
![y+\frac{2}{y}-3<0](https://tex.z-dn.net/?f=y%2B%5Cfrac%7B2%7D%7By%7D-3%3C0)
- решим квадратное уравнение.
y1 = 1;
x1 = 0;
y2 = 2;
x2 = 1;
x ∈ (0;1);
(1/7+5/14)(4,5-7)
(2/14+5/14)*(-2,5)
7/14*(-2,5)
0,5*(-2,5)
-1,25
Разность прогрессии:
![\displaystyle\tt d=\frac{x_4-x_2}{4-2}= \frac{-10-70}{2}=-40](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ctt+d%3D%5Cfrac%7Bx_4-x_2%7D%7B4-2%7D%3D+%5Cfrac%7B-10-70%7D%7B2%7D%3D-40)
Первый член:
![\displaystyle\tt x_1=x_2-d=70-(-40)=110](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ctt+x_1%3Dx_2-d%3D70-%28-40%29%3D110)
Сумма первых десяти членов :
![\displaystyle\tt S_{10}=\frac{2x_1+d(n-1)}{2}\cdot n=\frac{2\cdot110+(-40)(10-1)}{2}\cdot 10=\\\\{}~~~~=(220-360)\cdot5=-140\cdot5=-700](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ctt+S_%7B10%7D%3D%5Cfrac%7B2x_1%2Bd%28n-1%29%7D%7B2%7D%5Ccdot+n%3D%5Cfrac%7B2%5Ccdot110%2B%28-40%29%2810-1%29%7D%7B2%7D%5Ccdot+10%3D%5C%5C%5C%5C%7B%7D~~~~%3D%28220-360%29%5Ccdot5%3D-140%5Ccdot5%3D-700)