Question

For what values of $m$ is the inequality $\frac{x^2-mx-2}{x^2-3x+4}>-1$ satisfied for all $xϵR?$

Answer 1

$\frac{x^2-mx-2}{x^2-3x+4}>1$ for all $x\in R$

$x^2-mx-2>-x^2+3x-4$

$2x^2-(m+3)x+2>0$

$\therefore △<0$

$(m+3{)}^2-\mathrm{4.2.2}<0$

$m^2+6m+9-16<0$

$m^2+6m-7<0$

$(m+7)(m-1)<0$

$m\in (-7,1)$