In base $b,$ the square of the number $17_b$ is $211_b$. Find the base $b$.

onyuIee Aug 27, 2024

#1**0 **

\(b + 7 = 2b^2+b+1\)

\(2b^2 = 6\)

\(b^2 = 3\)

\(\mathbf{b = \sqrt{3}}\)

But since sqrt(3) < 7, the base wouldn't work for the left side of the equation. Therefore, **there is no solution.**

Maxematics Aug 27, 2024