![x^2+2x-5=0\\ D=4+4*1*5=\sqrt{24}\\ x_{1}=\frac{-2+\sqrt{24}}{2}\\ x_{2}=\frac{-2-\sqrt{24}}{2}\\ ](https://tex.z-dn.net/?f=x%5E2%2B2x-5%3D0%5C%5C%0AD%3D4%2B4%2A1%2A5%3D%5Csqrt%7B24%7D%5C%5C%0Ax_%7B1%7D%3D%5Cfrac%7B-2%2B%5Csqrt%7B24%7D%7D%7B2%7D%5C%5C%0Ax_%7B2%7D%3D%5Cfrac%7B-2-%5Csqrt%7B24%7D%7D%7B2%7D%5C%5C%0A)
тогда обратные к этим корням будут корни
![x_{1}=\frac{-2+\sqrt{24}}{2}\\ x_{2}=\frac{-2-\sqrt{24}}{2}\\\\ \frac{1}{x_{1}}=\frac{2}{-2+\sqrt{24}}\\ \frac{1}{x_{2}}=\frac{2}{-2-\sqrt{24}}\\ ](https://tex.z-dn.net/?f=x_%7B1%7D%3D%5Cfrac%7B-2%2B%5Csqrt%7B24%7D%7D%7B2%7D%5C%5C%0Ax_%7B2%7D%3D%5Cfrac%7B-2-%5Csqrt%7B24%7D%7D%7B2%7D%5C%5C%5C%5C%0A%5Cfrac%7B1%7D%7Bx_%7B1%7D%7D%3D%5Cfrac%7B2%7D%7B-2%2B%5Csqrt%7B24%7D%7D%5C%5C%0A%5Cfrac%7B1%7D%7Bx_%7B2%7D%7D%3D%5Cfrac%7B2%7D%7B-2-%5Csqrt%7B24%7D%7D%5C%5C%0A)
тогда уравнение примет в вид
![\frac{1}{x_{1}}=\frac{2}{-2+\sqrt{24}}\\ \frac{1}{x_{2}}=\frac{2}{-2-\sqrt{24}}\\ y=\frac{1}{x_{1}}\\ y=\frac{1}{x_{2}}\\ (y-\frac{2}{-2+\sqrt{24}})(y-\frac{2}{-2-\sqrt{24}})=y^2-0.4y-0.2\\ y=x\\ x^2-0.4x-0.2=0](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7Bx_%7B1%7D%7D%3D%5Cfrac%7B2%7D%7B-2%2B%5Csqrt%7B24%7D%7D%5C%5C+%0A%5Cfrac%7B1%7D%7Bx_%7B2%7D%7D%3D%5Cfrac%7B2%7D%7B-2-%5Csqrt%7B24%7D%7D%5C%5C%0Ay%3D%5Cfrac%7B1%7D%7Bx_%7B1%7D%7D%5C%5C%0Ay%3D%5Cfrac%7B1%7D%7Bx_%7B2%7D%7D%5C%5C%0A%28y-%5Cfrac%7B2%7D%7B-2%2B%5Csqrt%7B24%7D%7D%29%28y-%5Cfrac%7B2%7D%7B-2-%5Csqrt%7B24%7D%7D%29%3Dy%5E2-0.4y-0.2%5C%5C%0Ay%3Dx%5C%5C%0Ax%5E2-0.4x-0.2%3D0)
0,4+0,5=0,9
4 в -1 степени=4/10=0,4
5 в -1 степени=5/10=0,5
1) Корень 3-й степени, значит под знаком корня может быть отрицательное число. Но на 0 делить нельзя.
Область определения:
![x-1\neq 0\\x\neq1\\\boxed{x\in(-\infty;1)\text{U}(1;+\infty)}](https://tex.z-dn.net/?f=x-1%5Cneq%200%5C%5Cx%5Cneq1%5C%5C%5Cboxed%7Bx%5Cin%28-%5Cinfty%3B1%29%5Ctext%7BU%7D%281%3B%2B%5Cinfty%29%7D)
2) Тут снова дробь. На 0 делить нельзя.
Область определения:
![x+2\neq 0\\x\neq -2\\\boxed{x\in(-\infty;-2)\text{U}(-2;+\infty)}](https://tex.z-dn.net/?f=x%2B2%5Cneq%200%5C%5Cx%5Cneq%20-2%5C%5C%5Cboxed%7Bx%5Cin%28-%5Cinfty%3B-2%29%5Ctext%7BU%7D%28-2%3B%2B%5Cinfty%29%7D)
![a=4;b=13;c=15](https://tex.z-dn.net/?f=a%3D4%3Bb%3D13%3Bc%3D15)
полупериметр равен
![p=\frac{a+b+c}{2}=\frac{4+13+15}{2}=16](https://tex.z-dn.net/?f=p%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%3D%5Cfrac%7B4%2B13%2B15%7D%7B2%7D%3D16)
площадь треугольника по формуле Герона-Архимеда
![S=\sqrt{p((p-a)(p-b)(p-c)}=\sqrt{16*(16-4)*(16-13)*(16-15)}=24](https://tex.z-dn.net/?f=S%3D%5Csqrt%7Bp%28%28p-a%29%28p-b%29%28p-c%29%7D%3D%5Csqrt%7B16%2A%2816-4%29%2A%2816-13%29%2A%2816-15%29%7D%3D24)
радиус описанной окружности
![R=\frac{abc}{4S}=\frac{4*13*15}*{4*24}=8.125](https://tex.z-dn.net/?f=R%3D%5Cfrac%7Babc%7D%7B4S%7D%3D%5Cfrac%7B4%2A13%2A15%7D%2A%7B4%2A24%7D%3D8.125)
Длина окружности
![C=2*\pi*R \approx 2*3.14*8.125 \approx 51.025](https://tex.z-dn.net/?f=C%3D2%2A%5Cpi%2AR%20%5Capprox%202%2A3.14%2A8.125%20%5Capprox%2051.025)
ответ: 51.025 см