Question

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

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (D)

3

Answer 2

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.