In base $b,$ the square of the number $17_b$ is $211_b$. Find the base $b$.
(x+7)^2=2x^2+x+1:Converting to base 10
x^2+49+14x=2x^2+x+1:Using the formula (a+b)^2 = a^2+b^2+2ab
x^2=13x+48
x=16
So the answer is 16
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