Задание 6, стр 48

Question

Решите уравнение.
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a) $4 x^2=8$
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b) $\frac{x^2}{25}-4=5$
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c) $7 x^2-10=18$
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d) $6 x^2+3 x=3 x^2-x$
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e) $2 x^2-18=3 x^2+7$
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f) $x^2=2 x^2+2 x$

Gimli · Accepted Answer

\begin{enumerate} [label=\alph*)]
\item $4 x^2=8$
ewline $x^2=\frac{8}{4}$
ewline $x^2=2$
ewline $x=\pm \sqrt{2}$
\item $\frac{x^2}{25}-4=5(\cdot 25)$
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$x^2-4 \cdot 25=5 \cdot 25$
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$x^2-100=125$
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$x^2=125+100$
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$x^2=225$
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$x=\pm15$.
\item  $7 x^2-10=18$
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$7 x^2=18+10$
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$7 x^2=28$
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$x^2=\frac{28}{7}$
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$x^2=4$
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$x=\pm 2$.
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\item $6 x^2+3 x=3 x^2-x$
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$6 x^2-3 x^2+3 x+x=0$
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$3 x^2+4 x=0$
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$x(3 x+4)=0$
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$
\left\{\begin{array} { l } 
{ x = 0 } \
{ 3 x + 4 = 0 }
\end{array} \quad\left\{\begin{array} { l } 
{ x = 0 } \
{ 3 x = - 4 }
\end{array} \quad\left\{\begin{array}{l}
x=0 \
x=-\frac{4}{3}
\end{array}ight.ight.ight.
$
\item $2 x^2+18=3 x^2+7$
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$2 x^2-3 x^2=7+18$
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$-x^2=25$
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$x^2=-25$
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$x \in\{\varnothing\}$
\item $x^2=2 x^2+2 x$
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$x^2-2 x^2=2 x$
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$-x^2=2 x$
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$-x^2-2 x=0$
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$x^2+2 x=0$
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$x(x+2)=0$
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$\left\{\begin{array}{l}x=0 \ x+2=0\end{array} \quad\left\{\begin{array}{l}x=0 \ x=-2 .\end{array}ight.ight.$
\end{enumerate}

Задание 6, стр 48

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Задание 6, стр 48

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