Реши задание на изображении

Вот решения всех 14 примеров.

1. \[ 2x^2-5x+3=0 \] \[ (2x-3)(x-1)=0 \] \[ \boxed{x_1=1,\quad x_2=\frac32} \]

2. \[ x^2+3x+2=0 \] \[ (x+1)(x+2)=0 \] \[ \boxed{x_1=-1,\quad x_2=-2} \]

3. \[ 2x^2-9x+4=0 \] \[ (2x-1)(x-4)=0 \] \[ \boxed{x_1=\frac12,\quad x_2=4} \]

4. \[ 3x^2+8x-3=0 \] \[ (3x-1)(x+3)=0 \] \[ \boxed{x_1=\frac13,\quad x_2=-3} \]

5. \[ -x^2+7x-10=0 \] \[ -(x-5)(x-2)=0 \] \[ \boxed{x_1=2,\quad x_2=5} \]

6. \[ 4x^2+4x+1=0 \] \[ (2x+1)^2=0 \] \[ \boxed{x=-\frac12} \] Корень двукратный.

7. \[ x^2-6x-16=0 \] \[ (x-8)(x+2)=0 \] \[ \boxed{x_1=8,\quad x_2=-2} \]

8. \[ x^2+2x-15=0 \] \[ (x+5)(x-3)=0 \] \[ \boxed{x_1=3,\quad x_2=-5} \]

9. \[ 6x^2-7x+1=0 \] \[ (6x-1)(x-1)=0 \] \[ \boxed{x_1=\frac16,\quad x_2=1} \]

10. \[ 7x^2+9x+2=0 \] \[ (7x+2)(x+1)=0 \] \[ \boxed{x_1=-\frac27,\quad x_2=-1} \]

11. \[ x^2+4x-45=0 \] \[ (x+9)(x-5)=0 \] \[ \boxed{x_1=5,\quad x_2=-9} \]

12. \[ x^2+x-6=0 \] \[ (x+3)(x-2)=0 \] \[ \boxed{x_1=2,\quad x_2=-3} \]

13. \[ x^2+3x+2=0 \] \[ (x+1)(x+2)=0 \] \[ \boxed{x_1=-1,\quad x_2=-2} \]

14. \[ x^2+4x-5=0 \] \[ (x+5)(x-1)=0 \] \[ \boxed{x_1=1,\quad x_2=-5} \]

Полные ответы:

1. \(x_1=1,\quad x_2=\frac{3}{2}\)
2. \(x_1=-1,\quad x_2=-2\)
3. \(x_1=\frac{1}{2},\quad x_2=4\)
4. \(x_1=\frac{1}{3},\quad x_2=-3\)
5. \(x_1=2,\quad x_2=5\)
6. \(x_1=x_2=-\frac{1}{2}\)
7. \(x_1=8,\quad x_2=-2\)
8. \(x_1=3,\quad x_2=-5\)
9. \(x_1=\frac{1}{6},\quad x_2=1\)
10. \(x_1=-\frac{2}{7},\quad x_2=-1\)
11. \(x_1=5,\quad x_2=-9\)
12. \(x_1=2,\quad x_2=-3\)
13. \(x_1=-1,\quad x_2=-2\)
14. \(x_1=1,\quad x_2=-5\)

Использую те же 14 уравнений. Как на фото:

\[ D=b^2-4ac,\qquad x_1=\frac{-b+\sqrt D}{2a},\qquad x_2=\frac{-b-\sqrt D}{2a}. \]

1.

\[ 2x^2-5x+3=0 \] \[ D=(-5)^2-4\cdot2\cdot3=25-24=1 \] \[ x_1=\frac{5+1}{4}=\frac{6}{4}=\frac32 \] \[ x_2=\frac{5-1}{4}=\frac44=1 \]

\[ \boxed{x_1=\frac32,\quad x_2=1} \]

2.

\[ x^2+3x+2=0 \] \[ D=3^2-4\cdot1\cdot2=9-8=1 \] \[ x_1=\frac{-3+1}{2}=-1 \] \[ x_2=\frac{-3-1}{2}=-2 \]

\[ \boxed{x_1=-1,\quad x_2=-2} \]

3.

\[ 2x^2-9x+4=0 \] \[ D=(-9)^2-4\cdot2\cdot4=81-32=49 \] \[ x_1=\frac{9+7}{4}=\frac{16}{4}=4 \] \[ x_2=\frac{9-7}{4}=\frac24=\frac12 \]

\[ \boxed{x_1=4,\quad x_2=\frac12} \]

4.

\[ 3x^2+8x-3=0 \] \[ D=8^2-4\cdot3\cdot(-3)=64+36=100 \] \[ x_1=\frac{-8+10}{6}=\frac26=\frac13 \] \[ x_2=\frac{-8-10}{6}=\frac{-18}{6}=-3 \]

\[ \boxed{x_1=\frac13,\quad x_2=-3} \]

5.

\[ -x^2+7x-10=0 \] \[ D=7^2-4\cdot(-1)\cdot(-10)=49-40=9 \] \[ x_1=\frac{-7+3}{-2}=\frac{-4}{-2}=2 \] \[ x_2=\frac{-7-3}{-2}=\frac{-10}{-2}=5 \]

\[ \boxed{x_1=2,\quad x_2=5} \]

6.

\[ 4x^2+4x+1=0 \] \[ D=4^2-4\cdot4\cdot1=16-16=0 \] \[ x_1=\frac{-4+0}{8}=-\frac12 \] \[ x_2=\frac{-4-0}{8}=-\frac12 \]

\[ \boxed{x_1=x_2=-\frac12} \]

7.

\[ x^2-6x-16=0 \] \[ D=(-6)^2-4\cdot1\cdot(-16)=36+64=100 \] \[ x_1=\frac{6+10}{2}=8 \] \[ x_2=\frac{6-10}{2}=-2 \]

\[ \boxed{x_1=8,\quad x_2=-2} \]

8.

\[ x^2+2x-15=0 \] \[ D=2^2-4\cdot1\cdot(-15)=4+60=64 \] \[ x_1=\frac{-2+8}{2}=3 \] \[ x_2=\frac{-2-8}{2}=-5 \]

\[ \boxed{x_1=3,\quad x_2=-5} \]

9.

\[ 6x^2-7x+1=0 \] \[ D=(-7)^2-4\cdot6\cdot1=49-24=25 \] \[ x_1=\frac{7+5}{12}=\frac{12}{12}=1 \] \[ x_2=\frac{7-5}{12}=\frac{2}{12}=\frac16 \]

\[ \boxed{x_1=1,\quad x_2=\frac16} \]

10.

\[ 7x^2+9x+2=0 \] \[ D=9^2-4\cdot7\cdot2=81-56=25 \] \[ x_1=\frac{-9+5}{14}=\frac{-4}{14}=-\frac27 \] \[ x_2=\frac{-9-5}{14}=\frac{-14}{14}=-1 \]

\[ \boxed{x_1=-\frac27,\quad x_2=-1} \]

11.

\[ x^2+4x-45=0 \] \[ D=4^2-4\cdot1\cdot(-45)=16+180=196 \] \[ x_1=\frac{-4+14}{2}=\frac{10}{2}=5 \] \[ x_2=\frac{-4-14}{2}=\frac{-18}{2}=-9 \]

\[ \boxed{x_1=5,\quad x_2=-9} \]

12.

\[ x^2+x-6=0 \] \[ D=1^2-4\cdot1\cdot(-6)=1+24=25 \] \[ x_1=\frac{-1+5}{2}=2 \] \[ x_2=\frac{-1-5}{2}=-3 \]

\[ \boxed{x_1=2,\quad x_2=-3} \]

13.

\[ x^2+3x+2=0 \] \[ D=3^2-4\cdot1\cdot2=9-8=1 \] \[ x_1=\frac{-3+1}{2}=-1 \] \[ x_2=\frac{-3-1}{2}=-2 \]

\[ \boxed{x_1=-1,\quad x_2=-2} \]

14.

\[ x^2+4x-5=0 \] \[ D=4^2-4\cdot1\cdot(-5)=16+20=36 \] \[ x_1=\frac{-4+6}{2}=1 \] \[ x_2=\frac{-4-6}{2}=-5 \]

\[ \boxed{x_1=1,\quad x_2=-5} \]