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

 Jul 5, 2024
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(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

 Jul 5, 2024

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