SOLUTION: a number is written 52 base x.four times the number is written as 301 base x.what is x?

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Question 1140534: a number is written 52 base x.four times the number is written as 301 base x.what is x?
Answer by ikleyn(52825) About Me  (Show Source):
You can put this solution on YOUR website!
.

4*(5x+2) = 3x^2 + 1


3x^2 - 20x - 7 = 0


x%5B1%2C2%5D = %2820+%2B-+sqrt%2820%5E2+%2B+4%2A3%2A7%29%29%2F%282%2A3%29 = %2820+%2B-+sqrt%28484%29%29%2F6 = %2820+%2B-+22%29%2F6.


Only positive root makes sense  x = %2820+%2B+22%29%2F6 = 42%2F6 = 7.


ANSWER.  The base is 7.