Here's a problem about perfect squares and it's very hard for me. I tried to solve but I got stuck.
Last year, the town of Whipple had a population that was a perfect square. Last month, 100 enlightened people moved to Whipple, making the population one more than a perfect square. Next month, 100 more people will move to Whipple, making the population a perfect square again. What was the original population of Whipple?
Here's what I did:
Let the population last year be n, so n = x^2 and x = √n
Last month: n + 100 = x^2 + 1
Next Month: n + 200 = x^2 …
and i Got stuck there. I don't know where I am going … Your help is appreciated
Best Answer
Be careful with your variable names; it will clarify things for you. You've used $x$ to mean three different things!
Let $n=x^2$; then $n+200=y^2$, so that $x^2+200 = y^2$. Rewriting gives $y^2-x^2=(y-x)(y+x)=200$. Can you make progress from there?