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