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Math Help - I'm so lost...please help?!

  1. #1
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    I'm so lost...please help?!

    Augustus De Morgan was alive during the nineteenth century and once wrote, "I was x years old in the year x^2." what was the year of his birth?

    How do you even figure this out? Where do you even start?
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  2. #2
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    Hello, t-lee!

    Augustus De Morgan was alive during the nineteenth century
    and once wrote, "I was x years old in the year x^2."
    What was the year of his birth?

    How do you even figure this out? Where do you even start?

    If you're waiting for a magical "Squared-age Formula", better sit down.

    I assume that he was born in the 1800's.
    . . Hence: .x > 1800

    Care to try some numbers?

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  3. #3
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    Once I start putting numbers into x^2 > 1800 what am I looking for? I am confused with that. I realize I'm looking for the year he was born, but how do I know when I have found it?
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  4. #4
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    Quote Originally Posted by t-lee View Post
    Once I start putting numbers into x^2 > 1800 what am I looking for? I am confused with that. I realize I'm looking for the year he was born, but how do I know when I have found it?
    You start making a list of possible values of x that make sense as "how old is a person" that give an x^2 between 1800 and 1900. I only found one possibility.

    -Dan
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  5. #5
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    Tell me if I'm close or right on this...

    is 42^2 = 1764
    43^2 = 1849
    44^2 = 1936

    So he was 43 (x years old) in the yeas 1849 (x^2)
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  6. #6
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    Quote Originally Posted by t-lee View Post
    Tell me if I'm close or right on this...

    is 42^2 = 1764
    43^2 = 1849
    44^2 = 1936

    So he was 43 (x years old) in the yeas 1849 (x^2)
    Yes
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  7. #7
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    Quote Originally Posted by t-lee View Post
    Augustus De Morgan was alive during the nineteenth century and once wrote, "I was x years old in the year x^2." what was the year of his birth?

    How do you even figure this out? Where do you even start?
    1800<=x^2<=1899,

    so

    sqrt(1800)<x<sqrt(1899)

    or:

    42.43<x<43.58.

    But x is an integer, and the only integer satisfying this constraint is 43.

    RonL
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  8. #8
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    Thanks

    I figure that the year he was born was 1806

    If I subtract 1849 from his age of 43.

    Thank you all so much for your help!

    t-lee
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