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All the values of $m$ for which both roots of the equations $x^2-2 m x+m^2-1=0$ are greater than $-2$ but less than 4 , lie in the interval
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Verified Answer
The correct answer is:
−1 < m < 3
−1 < m < 3
Equation $x^2-2 m x+m^2-1=0$
$$
\begin{aligned}
& (x-m)^2-1=0 \\
& (x-m+1)(x-m-1)=0 \\
& x=m-1, m+1 \\
& -2 < m-1 \text { and } m+1 < 4
\end{aligned}
$$
$m>-1$ and $m < 3$
$-1 < m < 3$
$$
\begin{aligned}
& (x-m)^2-1=0 \\
& (x-m+1)(x-m-1)=0 \\
& x=m-1, m+1 \\
& -2 < m-1 \text { and } m+1 < 4
\end{aligned}
$$
$m>-1$ and $m < 3$
$-1 < m < 3$
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