Question

The number of integral solution of \(\frac{x + 1}{x^2 + 2}>\frac{1}{4}\) is

• A. 1
• B. 2
• C. 5
• D. None of these

Hint:

Check denominator positive: \(x^2 + 2>0\) always.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Solve inequality.
Step 2: Detailed Explanation:
\(\frac{x + 1}{x^2 + 2}>\frac{1}{4}\)
\(4(x + 1)>x^2 + 2 \rightarrow 4x + 4>x^2 + 2 \rightarrow 0>x^2 - 4x - 2\)
\(x^2 - 4x - 2<0\)
Roots: \(2 \pm \sqrt{6} \approx 2 \pm 2.449 \rightarrow -0.449<x<4.449\)
Integers: 0, 1, 2, 3, 4 \(\rightarrow\) 5 solutions.
Step 3: Final Answer:
5 integral solutions.