Question

Решить квадратные уравнения
a) x^2-2x-8=0
b) x^2+6x+9=0
c) x^2-8x=0
d) 2x^2+3x=9
e) x^2+3x+7=0
f) 32-2x^2=0

Answer 1

Ответ:

а

${x}^{2} - 2x - 8 = 0 \\ D= 4 + 32 = 36 \\ x_1 = \frac{2 + 6}{2} = 4 \\ x_2 = - 2$

б

${x}^{2} + 6x + 9 = 0 \\ {(x + 3)}^{2} = 0 \\ x = - 3$

с

${x}^{2} - 8x = 0 \\ x(x - 8) = 0 \\ x_1 = 0 \\ \\ x - 8 = 0 \\ x_2 = 8$

d

$2 {x}^{2} + 3x = 9 \\ 2 {x}^{2} + 3x - 9 = 0 \\ D = 9 + 4 \times 18 = 9 + 72 = 81 \\ x_1 = \frac{ - 3 + 9}{4} = 1.5 \\ x_2 = - 3$

e

${x}^{2} + 3x + 7 = 0 \\ D = 9 - 28 < 0$

нет корней

f

$32 - 2 {x}^{2} = 0 \\ 2(16 - {x}^{2} ) = 0 \\ 16 - {x}^{2} = 0 \\ {x}^{2} = 16 \\ x = \pm4$

Answer 2

Ответ:

а

\begin{gathered} {x}^{2} - 2x - 8 = 0 \\ D= 4 + 32 = 36 \\ x_1 = \frac{2 + 6}{2} = 4 \\ x_2 = - 2\end{gathered}

x

2

−2x−8=0

D=4+32=36

x

1

=

2

2+6

=4

x

2

=−2

б

\begin{gathered} {x}^{2} + 6x + 9 = 0 \\ {(x + 3)}^{2} = 0 \\ x = - 3\end{gathered}

x

2

+6x+9=0

(x+3)

2

=0

x=−3

с

\begin{gathered} {x}^{2} - 8x = 0 \\ x(x - 8) = 0 \\ x_1 = 0 \\ \\ x - 8 = 0 \\ x_2 = 8\end{gathered}

x

2

−8x=0

x(x−8)=0

x

1

=0

x−8=0

x

2

=8

d

\begin{gathered}2 {x}^{2} + 3x = 9 \\ 2 {x}^{2} + 3x - 9 = 0 \\ D = 9 + 4 \times 18 = 9 + 72 = 81 \\ x_1 = \frac{ - 3 + 9}{4} = 1.5 \\ x_2 = - 3\end{gathered}

2x

2

+3x=9

2x

2

+3x−9=0

D=9+4×18=9+72=81

x

1

=

4

−3+9

=1.5

x

2

=−3

e

\begin{gathered} {x}^{2} + 3x + 7 = 0 \\ D = 9 - 28 < 0\end{gathered}

x

2

+3x+7=0

D=9−28<0

нет корней

f

\begin{gathered}32 - 2 {x}^{2} = 0 \\ 2(16 - {x}^{2} ) = 0 \\ 16 - {x}^{2} = 0 \\ {x}^{2} = 16 \\ x = \pm4\end{gathered}

32−2x

2

=0

2(16−x

2

)=0

16−x

2

=0

x

2

=16

x=±4