Question

Number of integral solutions of $\frac{x+2}{x^2+1}>\frac{1}{2}$ is

• A. 0
• B. 1
• C. 2
• D. 3
• E. 4

Answer 1

Answer: (D)

Given that, $\frac{x+2}{x^2+1}>\frac{1}{2}$
$\Rightarrow$ $2x+4>x^2+1$
$\Rightarrow$ $x^2-2x-3<0$
$\Rightarrow$ $(x-3)(x+1)<0$
$\Rightarrow$ $-1<x<3$
The value of x are 0, 1, 2.
$\therefore$ The number of integral solutions is 3.