What is the base of the system in which 121 represents the same number as the decimal number 324?

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- Mar 19th 2007, 01:17 PMceasar_19134What is the base of the system...
What is the base of the system in which 121 represents the same number as the decimal number 324?

- Mar 19th 2007, 01:52 PMPlato
Solve b^2 + 2b + 1 = 324.

- Mar 28th 2007, 04:14 PMRimas
- Mar 28th 2007, 06:32 PMtopsquark
The number 121 in, say base 10, takes the form

1*10^2 + 2*10^1 + 1* 10^0 = 1*100 + 2*10 + 1 = 121

In a base "b" the number 121 represents:

1*b^2 + 2*b^1 + 1*b^0 = b^2 + 2b + 1

(So 121 in base 3 represents the decimal number 3^2 + 2*3 + 1 = 9 + 6 + 1 = 16.)

For this number to be equal to the decimal number 324 we must have

b^2 + 2b + 1 = 324

-Dan