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The image you uploaded contains a mathematical inequality involving square roots. Here's how it appears:

\[
2 \leq \sqrt{4x^2 - 4x + 1} - \sqrt{x^2 + 2x + 1} \leq 2,
\]
with the additional constraint:
\[
1 \leq x \leq 2.
\]

Let me solve this inequality step by step.

### Step 1: Simplify the Square Roots
- First square root: \(\sqrt{4x^2 - 4x + 1}\) can be simplified because the quadratic expression \(4x^2 - 4x + 1\) is a perfect square:
  \[
  \sqrt{4x^2 - 4x + 1} = \sqrt{(2x - 1)^2} = |2x - 1|.
  \]
  
- Second square

Solve the inequality: 2 ≤ √(4x^2 - 4x + 1) - √(x^2 + 2x + 1) ≤ 2 with the constraint 1 ≤ x ≤ 2.

Learn how to solve the inequality 2 ≤ √(4x^2 - 4x + 1) - √(x^2 + 2x + 1) ≤ 2 under the constraint 1 ≤ x ≤ 2. This problem covers key algebraic concepts such as simplifying square roots and solving inequalities, suitable for students in Grades 10-12.

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