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3 years ago

Please solve this

a1" title=" |x ^{2} + 3x - 1 | < 3" alt=" |x ^{2} + 3x - 1 | < 3" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

klasskru [66]3 years ago

8 0

$\bf |x^2+3x-1|\ \textless \ 3\implies 
\begin{cases}
+(x^2+3x-1)\ \textless \ 3\\\\
-(x^2+3x-1)\ \textless \ 3
\end{cases}\\\\
-------------------------------\\\\
x^2+3x-1\ \textless \ 3\implies x^2+3x-4\ \textless \ 0\implies (x+4)(x-1)\ \textless \ 0
\\\\\\
x\ \textless \ 
\begin{cases}
-4\\
1
\end{cases}\\\\
-------------------------------\\\\
-(x^2+3x-1)\ \textless \ 3\implies x^2+3x-1\boxed{\ \textgreater \ }-3
\\\\\\
x^2+3+2\ \textgreater \ 0\implies (x+2)(x+1)\ \textgreater \ 0\implies x\ \textgreater \ 
\begin{cases}
-2\\
-1
\end{cases}$

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