All the values of m for which both roots of the equation ${\mathrm{x}}^2-2\mathrm{mx}+{\mathrm{m}}^2-1=0$ are greater
than –2 but less than 4, lie in the interval

$\begin{array}{l}GivenEquation{x}^2-2mx+m^2-1=0\\ \therefore x=\frac{2m\pm \sqrt{4m^2-4(m^2-1)}}{2\left(1\right)}\\ =\frac{2m\pm \sqrt{4m^2-4m^2+4}}{2}\\ =\frac{2m\pm 2}{2}=m\pm 1\\ Givenbothrootslieb/w-2and4\\ -2<m+1<4and-2<m-1<4\\ \Rightarrow -3<m<3and-1<m<5\\ \therefore m\in (-1,3)\end{array}$