In base x system , 1/5 and (bar on 17)0.17 are numerals for the same number . Find x.

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1 answer

just as in base 10 .17 = 17/99 = 17/(10^2-1)
in base n,
.17 = (x+7)/(x^2-1) = 1/5
x = 9
check: .179 = 16/80 = 1/5