1 задача в 1 лежало 71.4 в 2 71.6
2 задача 120 учеников
4 завдання не до кінця розв'язане.
А).k=0,125 , y=19; k=2, y= -3; к=0,2 , y=0. б). k= -1/3, y= -1; k= -1, y= 18; k=2/3, y= -2 1/3. примеры идут по порядку.
![\sqrt[3]{2-x}=1-\sqrt{x-1}](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7B2-x%7D%3D1-%5Csqrt%7Bx-1%7D+++)
Возводим в куб
![2-x=1-3\sqrt{x-1}+3x-3-(x-1)\sqrt{x-1}\\ 4-4x=-\sqrt{x-1}(x+2)\\ -4(x-1)+\sqrt{x-1}(x+2)=0\\ \sqrt{x-1}(-4\sqrt{x-1} +x+2)=0\\ \\ \sqrt{x-1}=0\\ x-1=0\\ x=1\\ \\ x+2=4\sqrt{x-1}\\ x^2+4x+4=16x-16\\ x^2-12x+20=0\\ \frac{D}{4}=36-20=16=4^2\\ x_1=6-4=2\\ x_2=6+4=10](https://tex.z-dn.net/?f=+2-x%3D1-3%5Csqrt%7Bx-1%7D%2B3x-3-%28x-1%29%5Csqrt%7Bx-1%7D%5C%5C+++4-4x%3D-%5Csqrt%7Bx-1%7D%28x%2B2%29%5C%5C++-4%28x-1%29%2B%5Csqrt%7Bx-1%7D%28x%2B2%29%3D0%5C%5C++%5Csqrt%7Bx-1%7D%28-4%5Csqrt%7Bx-1%7D+%2Bx%2B2%29%3D0%5C%5C++%5C%5C+%5Csqrt%7Bx-1%7D%3D0%5C%5C++x-1%3D0%5C%5C+x%3D1%5C%5C+%5C%5C+x%2B2%3D4%5Csqrt%7Bx-1%7D%5C%5C++x%5E2%2B4x%2B4%3D16x-16%5C%5C+x%5E2-12x%2B20%3D0%5C%5C+%5Cfrac%7BD%7D%7B4%7D%3D36-20%3D16%3D4%5E2%5C%5C++x_1%3D6-4%3D2%5C%5C+x_2%3D6%2B4%3D10+)
Проверка на посторонние корни:
![\sqrt[3]{2-1}=1-\sqrt{1-1}\\ 1=1\\ \\ \sqrt[3]{2-2}=1-\sqrt{2-1}\\ 0=0\\ \\ \sqrt[3]{2-10}=1-\sqrt{10-1} \\ -2=-2](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7B2-1%7D%3D1-%5Csqrt%7B1-1%7D%5C%5C+++1%3D1%5C%5C+%5C%5C+%5Csqrt%5B3%5D%7B2-2%7D%3D1-%5Csqrt%7B2-1%7D%5C%5C+++0%3D0%5C%5C+%5C%5C+%5Csqrt%5B3%5D%7B2-10%7D%3D1-%5Csqrt%7B10-1%7D++%5C%5C+-2%3D-2+)
Ответ: 1; 2; 10
6)(2x+3)^2-(x-2)^2=5
4x^2+12x+9-x^2+4x-4-5=0
3x^2+16x=0
x(3x+16)=0
x=0
3x=-16
x=-16/3
7)y=x^2, y=kx-1
x^2=kx-1
x^2-kx+1=0
D=k^2-4
k^2-4=0
k^2=4
k1=2
K2=-2