Б)4х²-12х+9-8х-4х²=11
-20х+9-11=0
-20х-2=0
-20х=2
х=<u /><em />-2/20 (ну две двадцатых)
г)12х+16х²-9-12х-16х²+2х=0 (подобные члены вычеркиваются)
-9+2х=0
2х=9
х=4,5
1) Воспользуемся теоремой Виета:
![x^2+x-a=0\; ,\; \; x_1=4\\\\Teorema\; Vieta:\; \; \; x_1+x_2=-1\; \; \to \; \; 4+x_2=-1\; ,\; x_2=-5\\\\.\qquad \qquad \qquad x_1\cdot x_2=-a\; \; \to \; \; -1\cdot (-5)=-a\; ,\; \; a=-5](https://tex.z-dn.net/?f=x%5E2%2Bx-a%3D0%5C%3B+%2C%5C%3B+%5C%3B+x_1%3D4%5C%5C%5C%5CTeorema%5C%3B+Vieta%3A%5C%3B+%5C%3B+%5C%3B+x_1%2Bx_2%3D-1%5C%3B+%5C%3B+%5Cto+%5C%3B+%5C%3B+4%2Bx_2%3D-1%5C%3B+%2C%5C%3B+x_2%3D-5%5C%5C%5C%5C.%5Cqquad+%5Cqquad+%5Cqquad+x_1%5Ccdot+x_2%3D-a%5C%3B+%5C%3B+%5Cto+%5C%3B+%5C%3B+-1%5Ccdot+%28-5%29%3D-a%5C%3B+%2C%5C%3B+%5C%3B+a%3D-5)
2) Сторона прямоугольника = х см, вторая сторона = (х+1,5) .
Площадь равна х*(х+1,5)=10
х²+1,5х=10
2х²+3х-20=0
D=169 , x=-4<0 не подходит
x=5/2
х+1,5=5/2+3/2=8/2=4
Подынтегральная функция существует на [1;+∞)
![\displaystyle \int\limits^{+\infty}_1\frac{dx}{x^2+x}=\int\limits^{+\infty}_1(\frac{1}{x}-\frac{1}{x+1})dx= \lim_{b \to +\infty}(ln|\frac{x}{x+1}|)|^b_1=\\=\lim_{b \to +\infty}(ln|\frac{b}{b+1}|)-ln\frac{1}{2}=\lim_{b \to +\infty}ln|\frac{1}{1+\frac{1}{b}^{\to0}}|-ln\frac{1}{2}=-ln\frac{1}{2}\approx0,693](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cint%5Climits%5E%7B%2B%5Cinfty%7D_1%5Cfrac%7Bdx%7D%7Bx%5E2%2Bx%7D%3D%5Cint%5Climits%5E%7B%2B%5Cinfty%7D_1%28%5Cfrac%7B1%7D%7Bx%7D-%5Cfrac%7B1%7D%7Bx%2B1%7D%29dx%3D+%5Clim_%7Bb+%5Cto+%2B%5Cinfty%7D%28ln%7C%5Cfrac%7Bx%7D%7Bx%2B1%7D%7C%29%7C%5Eb_1%3D%5C%5C%3D%5Clim_%7Bb+%5Cto+%2B%5Cinfty%7D%28ln%7C%5Cfrac%7Bb%7D%7Bb%2B1%7D%7C%29-ln%5Cfrac%7B1%7D%7B2%7D%3D%5Clim_%7Bb+%5Cto+%2B%5Cinfty%7Dln%7C%5Cfrac%7B1%7D%7B1%2B%5Cfrac%7B1%7D%7Bb%7D%5E%7B%5Cto0%7D%7D%7C-ln%5Cfrac%7B1%7D%7B2%7D%3D-ln%5Cfrac%7B1%7D%7B2%7D%5Capprox0%2C693)
Подынтегральная функция не существует в точке х=0
![\displaystyle \int\limits^{0}_{-1}\frac{dx}{x^3}= \lim_{b \to 0-0} (-\frac{1}{2x^2})|^b_{-1}=\lim_{b \to 0-0}(-\frac{1}{2(0-0)^2})+\frac{1}{2}=-\infty+\frac{1}{2}=\\=-\infty](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cint%5Climits%5E%7B0%7D_%7B-1%7D%5Cfrac%7Bdx%7D%7Bx%5E3%7D%3D+%5Clim_%7Bb+%5Cto+0-0%7D+%28-%5Cfrac%7B1%7D%7B2x%5E2%7D%29%7C%5Eb_%7B-1%7D%3D%5Clim_%7Bb+%5Cto+0-0%7D%28-%5Cfrac%7B1%7D%7B2%280-0%29%5E2%7D%29%2B%5Cfrac%7B1%7D%7B2%7D%3D-%5Cinfty%2B%5Cfrac%7B1%7D%7B2%7D%3D%5C%5C%3D-%5Cinfty)
Интеграл расходится