Предмет: Алгебра,
автор: Жасмин1989
Помогите, пожалуйста!!! Надо решить неполные квадратные уравнения.
1) 5х=2-2х²
2) 12-х²=11
3) х²= - 4х
4) 5х²= - 2х
5) х²-6х=4х-25
6) х²+2х=16х-49
7) 3х²+9=12х-х²
8) 5х²+1=6х-4х²
9) х(х+2)=3
10) х(х+2)=4
Ответы
Автор ответа:
0
1)
![5x=2-2x^2 \ 2x^2+5x-2=0 \ D=25+16=41 \ x_1= frac{-5- sqrt{41} }{4} \ x_2= frac{-5+ sqrt{41} }{4} 5x=2-2x^2 \ 2x^2+5x-2=0 \ D=25+16=41 \ x_1= frac{-5- sqrt{41} }{4} \ x_2= frac{-5+ sqrt{41} }{4}](https://tex.z-dn.net/?f=5x%3D2-2x%5E2+%5C+2x%5E2%2B5x-2%3D0+%5C+D%3D25%2B16%3D41+%5C+x_1%3D+frac%7B-5-+sqrt%7B41%7D+%7D%7B4%7D+%5C+x_2%3D+frac%7B-5%2B+sqrt%7B41%7D+%7D%7B4%7D++)
2)
![12-x^2=11 \ x^2=1 \ x=pm1 12-x^2=11 \ x^2=1 \ x=pm1](https://tex.z-dn.net/?f=12-x%5E2%3D11+%5C+x%5E2%3D1+%5C+x%3Dpm1)
3)
![x^2=-4x \ x^2+4x=0 \ x(x+4)=0 \ x=0 \ x=-4 x^2=-4x \ x^2+4x=0 \ x(x+4)=0 \ x=0 \ x=-4](https://tex.z-dn.net/?f=x%5E2%3D-4x+%5C+x%5E2%2B4x%3D0+%5C+x%28x%2B4%29%3D0+%5C+x%3D0+%5C+x%3D-4)
4)
![5x^2=-2x \ 5x^2+2x=0 \ x(5x+2)=0 \ x=0 \ x=- frac{2}{5} 5x^2=-2x \ 5x^2+2x=0 \ x(5x+2)=0 \ x=0 \ x=- frac{2}{5}](https://tex.z-dn.net/?f=5x%5E2%3D-2x+%5C+5x%5E2%2B2x%3D0+%5C+x%285x%2B2%29%3D0+%5C+x%3D0+%5C+x%3D-+frac%7B2%7D%7B5%7D+)
5)
![x^2-6x=4x-25 \ x^2-10x+25=0 \ (x-5)^2=0 \ x=5 x^2-6x=4x-25 \ x^2-10x+25=0 \ (x-5)^2=0 \ x=5](https://tex.z-dn.net/?f=x%5E2-6x%3D4x-25+%5C+x%5E2-10x%2B25%3D0+%5C+%28x-5%29%5E2%3D0+%5C+x%3D5)
6)
![x^2+2x=16x-49 \ x^2-14x+49=0 \ (x-7)^2=0 \ x=7 x^2+2x=16x-49 \ x^2-14x+49=0 \ (x-7)^2=0 \ x=7](https://tex.z-dn.net/?f=x%5E2%2B2x%3D16x-49+%5C+x%5E2-14x%2B49%3D0+%5C+%28x-7%29%5E2%3D0+%5C+x%3D7)
7)
![3x^2+9=12x-x^2 \ 4x^2-12x+9=0 \ (2x-3)^2=0 \ 2x-3=0 \ 2x=3 \ x= frac{3}{2} 3x^2+9=12x-x^2 \ 4x^2-12x+9=0 \ (2x-3)^2=0 \ 2x-3=0 \ 2x=3 \ x= frac{3}{2}](https://tex.z-dn.net/?f=3x%5E2%2B9%3D12x-x%5E2+%5C+4x%5E2-12x%2B9%3D0++%5C+%282x-3%29%5E2%3D0+%5C+2x-3%3D0+%5C+2x%3D3+%5C+x%3D+frac%7B3%7D%7B2%7D+)
8)
![5x^2+1=6x-4x^2 \ 9x^2-6x+1=0 \ (3x-1)=0 \ 3x-1=0 \ 3x=1 \ x= frac{1}{3} 5x^2+1=6x-4x^2 \ 9x^2-6x+1=0 \ (3x-1)=0 \ 3x-1=0 \ 3x=1 \ x= frac{1}{3}](https://tex.z-dn.net/?f=5x%5E2%2B1%3D6x-4x%5E2+%5C+9x%5E2-6x%2B1%3D0+%5C+%283x-1%29%3D0+%5C+3x-1%3D0+%5C+3x%3D1+%5C+x%3D+frac%7B1%7D%7B3%7D+)
9)
![x(x+2)=3 \ x^2+2x=3 \ x^2+2x-3=0 \ D=4+12=16=4^2 \ x_1= frac{-2-4}{2}=-3 \ x_2= frac{-2+4}{2}=1 x(x+2)=3 \ x^2+2x=3 \ x^2+2x-3=0 \ D=4+12=16=4^2 \ x_1= frac{-2-4}{2}=-3 \ x_2= frac{-2+4}{2}=1](https://tex.z-dn.net/?f=x%28x%2B2%29%3D3+%5C+x%5E2%2B2x%3D3+%5C+x%5E2%2B2x-3%3D0+%5C+D%3D4%2B12%3D16%3D4%5E2+%5C+x_1%3D+frac%7B-2-4%7D%7B2%7D%3D-3+%5C+x_2%3D+frac%7B-2%2B4%7D%7B2%7D%3D1++)
10)
![x(x+2)=4 \ x^2+2x=4 \ x^2+2x-4=0 \ D=4+16=20=(2 sqrt{5})^2 \ x_{1,2}= frac{-2pm2 sqrt{5} }{2} (:2) \ x_{1,2}=-1pm sqrt{5} x(x+2)=4 \ x^2+2x=4 \ x^2+2x-4=0 \ D=4+16=20=(2 sqrt{5})^2 \ x_{1,2}= frac{-2pm2 sqrt{5} }{2} (:2) \ x_{1,2}=-1pm sqrt{5}](https://tex.z-dn.net/?f=x%28x%2B2%29%3D4+%5C+x%5E2%2B2x%3D4+%5C+x%5E2%2B2x-4%3D0+%5C+D%3D4%2B16%3D20%3D%282+sqrt%7B5%7D%29%5E2+%5C+x_%7B1%2C2%7D%3D+frac%7B-2pm2+sqrt%7B5%7D+%7D%7B2%7D+%28%3A2%29++%5C+x_%7B1%2C2%7D%3D-1pm+sqrt%7B5%7D+)
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