Not easy as you think
For the value(s) of (x,y) that satisfies the set of equations, find S such that S = |x + y|
The answer is 6.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
This is a bit of a "hack"-y solution, but it gets the job done and might make things a little less painful!
We are given that x 4 − y 4 = 2 4 0 , and we are looking for positive integer solutions. If we start listing out the fourth powers of positive integers 1 , 1 6 , 8 1 , 2 5 6 , 6 2 5 , … it looks somewhat clear that any x ≥ 5 could not give a y such that x 4 − y 4 ≤ 2 4 0 , since the "gaps" between the fourth powers "get too big". (Can you prove this?)
Looking over the powers we have, the only ones that subtract to 2 4 0 are 4 4 − 2 4 = 2 5 6 − 1 6 = 2 4 0 .
Now, all we need to do is verify that ( x , y ) = ( 4 , 2 ) satisfies the second equation (it does), and we're done!
Log in to reply
Exactly what sprang to my mind at first... I went to check people's solutions and couldn't believe how mind-boggling they made it to be! Anyway, I'm going to change the problem a little bit to make it more complicated for the "keen-eyed"
This problem might be an absolutely painful experience to some people, and even takes several days to solve. This is the shortest solution (in my opinion) to this problem. However, this solution is hard to figure out and definitely NOT recommendable. Any other solution is welcome