Question

Write the number of integral solutions of $\frac{x+2}{x^2+1}>\frac{1}{2}$

Answer 1

$\frac{x+2}{x^2+1}>\frac{1}{2}\Rightarrow 2x+4>x^2+1\Rightarrow 4>x^2-2x+1\Rightarrow 4>(x-1{)}^2\Rightarrow 2>|x-1|\Rightarrow 1-2<x<1+2\Rightarrow -1<x<3\Rightarrow xϵ(-1,3)\text{x can take values 0,1,2 as the integral solutions for}\frac{x+2}{x^2+1}>\frac{1}{2}\text{Hence,the number of integral solutions of}\frac{x+2}{x^2+1}>\frac{1}{2}is3$