(2х-11)/(3х-10) + (1-х)/(х-6)=0
<span>f(x)=x^3-2x^2+x+3
f`(x)=3x²-4x+1=3(x-1)(x-1/3)
3x²-4x+1=0
D=(-4)²-4*3*1=16-12=4=2²
x(1)=1
x(2)=1/3
f`(x)=0 при 3(x-1)(x-1/3)=0
+ - +
_________________1/3_____________1_____________
max min
x(max)=1/3 и х(min)=1 - стационарные точки</span>
1)
![2x^2-10=0 | :2 \\ x^2-5=0 \\ x^2- (\sqrt{5})^2=0](https://tex.z-dn.net/?f=2x%5E2-10%3D0+%7C+%3A2+%5C%5C+x%5E2-5%3D0++%5C%5C++x%5E2-+%28%5Csqrt%7B5%7D%29%5E2%3D0)
Используем формулу разности квадратов.
![( x- \sqrt{5})*(x+ \sqrt{5}) = 0](https://tex.z-dn.net/?f=%28+x-+%5Csqrt%7B5%7D%29%2A%28x%2B+%5Csqrt%7B5%7D%29+%3D+0++)
![x=+- \sqrt{5}](https://tex.z-dn.net/?f=x%3D%2B-+%5Csqrt%7B5%7D+)
Ответ:
![+-\sqrt{5}](https://tex.z-dn.net/?f=+%2B-%5Csqrt%7B5%7D+)
2)
![2x^2-10x=0 | :2 \\ x^2-5x=0 \\ x*(x-5)=0](https://tex.z-dn.net/?f=2x%5E2-10x%3D0+%7C+%3A2+%5C%5C+x%5E2-5x%3D0+%5C%5C+x%2A%28x-5%29%3D0)
![1) x=0; \\ \\ 2) x-5=0 \\ x=5](https://tex.z-dn.net/?f=1%29+x%3D0%3B++%5C%5C++%5C%5C+2%29+x-5%3D0++%5C%5C+x%3D5)
Ответ: 0; 5
3)
![2x^2-11x=0 \\ x*(2x-11)=0 \\ \\ 1)x=0 \\ \\ 2)2x-11=0 \\ 2x=11 \\ x=5,5](https://tex.z-dn.net/?f=2x%5E2-11x%3D0+%5C%5C++x%2A%282x-11%29%3D0++%5C%5C+%5C%5C+1%29x%3D0+%5C%5C++%5C%5C+2%292x-11%3D0+%5C%5C+2x%3D11+%5C%5C+x%3D5%2C5)
Ответ: 0; 5,5