![\sqrt{23} + \sqrt{23} - 8\sqrt{7} + 8 \sqrt{7} = 2 \sqrt{23}](https://tex.z-dn.net/?f=+%5Csqrt%7B23%7D++%2B++%5Csqrt%7B23%7D++-++8%5Csqrt%7B7%7D+++%2B+8+%5Csqrt%7B7%7D++%3D+2+%5Csqrt%7B23%7D)
а минус и плюс 8 корень 7 сокращается
![2 {n}^{2} + 11n + 12 = 0 \\ d = 121 - 4 \times 2 \times 12 = 121 - 96 = 25 \\ n1 = \frac{ - 11 + 5}{4} = - \frac{6}{4} = - 1.75 \\ n2 = \frac{ - 11 - 5}{4} = - 4](https://tex.z-dn.net/?f=2+%7Bn%7D%5E%7B2%7D++%2B+11n+%2B+12+%3D+0+%5C%5C+d+%3D+121+-+4+%5Ctimes+2+%5Ctimes+12+%3D+121+-+96+%3D+25+%5C%5C+n1+%3D++%5Cfrac%7B+-+11+%2B+5%7D%7B4%7D++%3D++-++%5Cfrac%7B6%7D%7B4%7D++%3D++-+1.75+%5C%5C+n2+%3D++%5Cfrac%7B+-+11+-+5%7D%7B4%7D++%3D++-+4+)
Получили два составных корня -1,75= - 5×0,35 и - 4= - 2×2 => выражение является составным
Вершина параболы:
у=х²+1
y'=2x
2x=0
x=0
y=0+1=1
(0;1)
ветви направлены вверх
строим второй график.
пересечение графиков (-2;5)(1;2)
пределы интеграла -2 и 1
![\int\limits^1_{-2} {x^2+1} \, dx = \frac{1}{3} x^3+x |_{-2} ^{1} =( \frac{1}{3} * 1^{3} +1)-( \frac{1}{3} (-2)^3-2)=](https://tex.z-dn.net/?f=+%5Cint%5Climits%5E1_%7B-2%7D+%7Bx%5E2%2B1%7D+%5C%2C+dx+%3D+%5Cfrac%7B1%7D%7B3%7D+x%5E3%2Bx++%7C_%7B-2%7D++%5E%7B1%7D+%3D%28+%5Cfrac%7B1%7D%7B3%7D+%2A+1%5E%7B3%7D+%2B1%29-%28+%5Cfrac%7B1%7D%7B3%7D+%28-2%29%5E3-2%29%3D+)
![= \frac{4}{3} + \frac{8}{3} +2=4+2=6](https://tex.z-dn.net/?f=%3D+%5Cfrac%7B4%7D%7B3%7D+%2B+%5Cfrac%7B8%7D%7B3%7D+%2B2%3D4%2B2%3D6)
![\int\limits^1_{-2} {-x+3} \, dx =- \frac{1}{2} x^{2} +3x |_{-2} ^{1} =(- \frac{1}{2} +3)-(-2-6)=2.5+8=10.5](https://tex.z-dn.net/?f=+%5Cint%5Climits%5E1_%7B-2%7D+%7B-x%2B3%7D+%5C%2C+dx+%3D-+%5Cfrac%7B1%7D%7B2%7D++x%5E%7B2%7D+%2B3x+%7C_%7B-2%7D++%5E%7B1%7D+%3D%28-+%5Cfrac%7B1%7D%7B2%7D+%2B3%29-%28-2-6%29%3D2.5%2B8%3D10.5)
S=10.5-6=4.5
2S=4.5*2=9
Ответ: 2S=9