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?

2. 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: .x² > 1800

Care to try some numbers?

3. 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?

4. Originally Posted by t-lee
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

5. 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)

6. Originally Posted by t-lee
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

7. Originally Posted by 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?
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

8. ## 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