Question

A={x€Z|√4x^2-4x+1<5 }

Answer 1

$A = \Big\{x\in \mathbb{Z} \Big| \sqrt{4x^2-4x+1} \ \textless \ 5} \Big\} \\ \\ \sqrt{4x^2-4x+1} \ \textless \ 5 \\ \\ \sqrt{(2x-1)^2} \ \textless \ 5 \\ \\ |2x-1| \ \textless \ 5 \\ \\ -5 \ \textless \ 2x -1 \ \textless \ 5 \Big|+1 \\ \\ -4 \ \textless \ 2x \ \textless \ 6 \Big|:2 \\ \\ -2 \ \textless \ x \ \textless \ 3 \\ \\ \Rightarrow A = \Big\{-1,0,1,2\Big\}$