toán nâng cao 10

L

lp_qt

bất phương trình $(m-1)x^2 +2x + m+1 >0$ nghiệm đúng \forall $m$

$\Longleftrightarrow \left\{\begin{matrix}m-1> 0 & \\ \Delta '=1-(m-1)(m+1)=2-m^{2}< 0 & \end{matrix}\right.$

$\Longleftrightarrow \left\{\begin{matrix}m>1 & \\ \begin{bmatrix}m> \sqrt{2} & \\ m<-\sqrt{2} & \end{bmatrix}& \end{matrix}\right.$

$\Longleftrightarrow m> \sqrt{2}$
 
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