#1**+2 **

We can start by replacing b with (a-1).

\begin{align*} (a-1)^2\cdot a^0&=7\cdot a^1+1\cdot a^0

\\\Rightarrow\qquad a^2-2a+1&=7a+1

\\\Rightarrow\qquad a^2-9a&=0

\\\Rightarrow\qquad a(a-9)&=0

\end{align*}

So we can have 0 or 9.

But there is no base 0, so must be base 9.

supermanaccz Mar 21, 2018