There are three consecutive positive integers such that the sum of the squares of the smallest two is 221. What are the numbers?
We can call the first number
The condition given here is that the square of the first number
Now we have two methods to solve this equation. One more mechanics, one more artistic.
The mechanics is to solve the second order equation
The artistic way is to write
and observe that we want that the product of two consecutive numbers has to be
For example we notice that we can write it as
Oh, it seems we found our consecutive numbers!