`x^2+1lt0`

Options

A. `-1lexle1`
B. `-1ltxlt0`
C. Does not exist
D. none of these

Answer

To solve the inequality \( x^2 + 1 < 0 \), we can follow these steps:

### Step 1: Analyze the inequality
We start with the inequality:
\[ x^2 + 1 < 0 \]

### Step 2: Rearrange the inequality
We can rearrange this inequality to isolate \( x^2 \):
\[ x^2 < -1 \]

### Step 3: Understand the implications
The expression \( x^2 \) represents the square of a real number. Since the square of any real number is always non-negative (i.e., \( x^2 \geq 0 \)), it is impossible for \( x^2 \) to be less than \(-1\).

### Step 4: Conclusion
Since there are no real numbers \( x \) such that \( x^2 < -1 \), we conclude that there are no solutions to the inequality:
\[ \text{No solution} \]

### Summary
The inequality \( x^2 + 1 < 0 \) has no real solutions because \( x^2 \) cannot be negative.

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