Hello everyone I am in year 9, and I have a question if you could help me answer it please thnx
The mathematician George enjoyed telling his friends he was x years old in the year x2. Find the year of Georges birth given he died in 1871 (rip George)
(note: what you're about to see is my full approach at tackling the problem. This is to illustrate how I might approach this problem, which is far more valuable than me just giving you the answer)
So, we need to find a number such that when squared, it gives a number less than 1871. What's a number that's less than 1871? Well, 1871-y is. So, let's set up that first equation:
1871-y=x
Now, let's apply some logic. While we don't know what age George died at, in the 19th century, you weren't going to live for a hell of a long time - so let's just say he couldn't have been born before 1800. This gives us some room to work with.
And this is where I'm not sure what my next logical step would be - so, let's try playing around. What are the list of squares that'll get you between 1800 and 1871?
10^2=100
20^2=400
30^2=900
40^2=1600
45^2=2025
Too far, let's go back
42^2=1764
43^2=1849
44^2=1936
Brilliant, there's only one age that fits - being 43 in 1849.
Since 1849-43=1806, we can say our good pal' George was born in 1806, living to ripe old age of 65.