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    What 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?
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    Solve b^2 + 2b + 1 = 324.
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    Quote Originally Posted by Plato View Post
    Solve b^2 + 2b + 1 = 324.
    How did you get that??
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ceasar_19134 View Post
    What is the base of the system in which 121 represents the same number as the decimal number 324?
    Quote Originally Posted by Plato View Post
    Solve b^2 + 2b + 1 = 324.
    Quote Originally Posted by Rimas View Post
    How did you get that??
    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
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