If $x_1$ and $x_2$ are the solutions of the equation $x^2-(m+3)x+m+2=0$ Find all real values of $m$ such that the following inequations are valid $\frac {1}{x_1}+\frac {1}{x_2}>\frac{1}{2}$ and $x_1^2+x_2^2<5$
Source: Kosovo MO 2009 Grade 10, Problem 2
Tags: inequalities
If $x_1$ and $x_2$ are the solutions of the equation $x^2-(m+3)x+m+2=0$ Find all real values of $m$ such that the following inequations are valid $\frac {1}{x_1}+\frac {1}{x_2}>\frac{1}{2}$ and $x_1^2+x_2^2<5$