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.