1)(a-2)²=a²-4a+4
2)(a-3)(a+3)=a²-9
3)(x-1)(x²+x+1)=x³-1
4)2.(c-2)(2+c)=2.(c²-4)=2c²-8
5)(x²+3)²=xˇ4 + 6x²+9
6)(a-3)(a+6)=a²+3a-18
Х²+4х-2 <(x+3)(x-3)
x²+4x-2<x²-9
4x< -7
x< -1 3/4
x< -2 (C)
А
54;45;36;27;18
Б
5/19;4/19;3/19;2/19;1/19
B
при делении на 5
9;14;19;24;29
при делении на 7
11;18;25;32
1. ![x^2-8x+17=0](https://tex.z-dn.net/?f=x%5E2-8x%2B17%3D0)
Дискриминант: D=64-4*17=64-68=-2<0 Корней нет
2.
Корень один х=-7
3. ![2x^2+17x+36=0](https://tex.z-dn.net/?f=2x%5E2%2B17x%2B36%3D0)
Дискриминант: D=289-4*2*36=289-288=1
![x_{1;2}=\frac{-17 \pm 1}{2*2} \ \ \ \ \ \ \ \ x_1=-4 \ \ \ \ \ x_2=-4.5](https://tex.z-dn.net/?f=x_%7B1%3B2%7D%3D%5Cfrac%7B-17%20%5Cpm%201%7D%7B2%2A2%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_1%3D-4%20%5C%20%5C%20%5C%20%5C%20%5C%20x_2%3D-4.5)
4. ![7x^2-3x-4=0](https://tex.z-dn.net/?f=7x%5E2-3x-4%3D0)
D=9-4*7*(-4)=9+112=121
![x_{1;2}=\frac{3 \pm 11}{2*7} \ \ \ \ \ \ \ \ x_1=1 \ \ \ \ \ x_2=-4/7](https://tex.z-dn.net/?f=x_%7B1%3B2%7D%3D%5Cfrac%7B3%20%5Cpm%2011%7D%7B2%2A7%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_1%3D1%20%5C%20%5C%20%5C%20%5C%20%5C%20x_2%3D-4%2F7)
5. ![9x^2+6x+1=0](https://tex.z-dn.net/?f=9x%5E2%2B6x%2B1%3D0)
D=36-36=0
![x=\frac{-6 \pm 0}{2*9}=-\frac{1}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%20%5Cpm%200%7D%7B2%2A9%7D%3D-%5Cfrac%7B1%7D%7B3%7D)
6. ![x^2=0.81](https://tex.z-dn.net/?f=x%5E2%3D0.81)
![x_{1;2}=\pm \sqrt{0.81}=\pm0.9](https://tex.z-dn.net/?f=x_%7B1%3B2%7D%3D%5Cpm%20%5Csqrt%7B0.81%7D%3D%5Cpm0.9)
7. ![9x^2+5x=0](https://tex.z-dn.net/?f=9x%5E2%2B5x%3D0)
![x(9x+5)=0 \ \ \ \ \ \ \ x_1=0 \ \ \ \ \ \ \ x_2=-5/9](https://tex.z-dn.net/?f=x%289x%2B5%29%3D0%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_1%3D0%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_2%3D-5%2F9)
8. ![8x^2-2x-1=0](https://tex.z-dn.net/?f=8x%5E2-2x-1%3D0)
D=4+32=36
![x_{1;2}=\frac{2 \pm 6}{2*8} \ \ \ \ \ \ \ \ x_1=0.5 \ \ \ \ \ x_2=-0.25](https://tex.z-dn.net/?f=x_%7B1%3B2%7D%3D%5Cfrac%7B2%20%5Cpm%206%7D%7B2%2A8%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_1%3D0.5%20%5C%20%5C%20%5C%20%5C%20%5C%20x_2%3D-0.25)
9. ![6x^2-19x+10=0](https://tex.z-dn.net/?f=6x%5E2-19x%2B10%3D0)
D=361-4*6*10=361-240=121
![x_{1;2}=\frac{19 \pm 11}{2*6} \ \ \ \ \ \ \ \ x_1=2.5 \ \ \ \ \ x_2=2/3](https://tex.z-dn.net/?f=x_%7B1%3B2%7D%3D%5Cfrac%7B19%20%5Cpm%2011%7D%7B2%2A6%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_1%3D2.5%20%5C%20%5C%20%5C%20%5C%20%5C%20x_2%3D2%2F3)
10. ![2x^2=-8](https://tex.z-dn.net/?f=2x%5E2%3D-8)
Корней нет, т.к. ![x^2\geq0](https://tex.z-dn.net/?f=x%5E2%5Cgeq0)
11. ![16x^2-40x+25=0](https://tex.z-dn.net/?f=16x%5E2-40x%2B25%3D0)
![(4x)^2-2*4*5x+5^2=0](https://tex.z-dn.net/?f=%284x%29%5E2-2%2A4%2A5x%2B5%5E2%3D0)
![(4x-5)^2=0](https://tex.z-dn.net/?f=%284x-5%29%5E2%3D0)
x=5/4=1.25
12. ![x^2-12x+36=0](https://tex.z-dn.net/?f=x%5E2-12x%2B36%3D0)
![x^2-2*6x+6^2=0](https://tex.z-dn.net/?f=x%5E2-2%2A6x%2B6%5E2%3D0)
![(x-6)^2=0](https://tex.z-dn.net/?f=%28x-6%29%5E2%3D0)
x=6
(y-1/3)(y+1/3)=0
y=1/3 U y=-1/3