Solve for x, if `sqrt(x^(2)-3x+2) lt x-2`

Explanation

To solve the inequality \( \sqrt{x^2 - 3x + 2} < x - 2 \), we will follow these steps:

### Step 1: Identify the conditions for the square root
The expression inside the square root must be non-negative:
\[ x^2 - 3x + 2 \geq 0 \]
Factoring the quadratic:
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