To find the error, we repeat the steps correctly:
i)
[tex]b=\frac{1}{2}\cdot\sqrt[]{a-1}[/tex]
ii) We pass the 2 dividing on the right, multiplicating at the left:
[tex]2b=\cdot\sqrt[]{a-1}[/tex]
iii) We take the square on both sides:
[tex]\begin{gathered} (2b)^2=(\sqrt[]{a-1})^2 \\ 2^2b^2=a-1 \\ 4b^2=a-1 \end{gathered}[/tex]
iv) Finally we pass the -1 on the right as +1 to the left:
[tex]4b^2+1=a[/tex]
Answer
Comparing the steps, we see that the error was in step III, the square of 2b is 4b², not 2b².
