Ответ:
а
б
с
d
e
нет корней
f
\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
1
=
2+6
=4
=−2
\begin{gathered} {x}^{2} + 6x + 9 = 0 \\ {(x + 3)}^{2} = 0 \\ x = - 3\end{gathered}
+6x+9=0
(x+3)
=0
x=−3
\begin{gathered} {x}^{2} - 8x = 0 \\ x(x - 8) = 0 \\ x_1 = 0 \\ \\ x - 8 = 0 \\ x_2 = 8\end{gathered}
−8x=0
x(x−8)=0
x−8=0
=8
\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
+3x=9
+3x−9=0
D=9+4×18=9+72=81
4
−3+9
=1.5
=−3
\begin{gathered} {x}^{2} + 3x + 7 = 0 \\ D = 9 - 28 < 0\end{gathered}
+3x+7=0
D=9−28<0
\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(16−x
)=0
16−x
=16
x=±4
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Answers & Comments
Ответ:
а
б
с
d
e
нет корней
f
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