Fun little math problem

[Dieter]

(05-10-2016 10:45 PM)Paul Dale Wrote:  I got the answer without a calculation aid in well under thirty seconds.
I'm several times 14 though.

How did you do it?

I have to admit I only got a (very) quick-and-dirty solution: Since x=(7–y)² and y=(11–x)² I assumed x and y to be the squares of integers, i.e. 4 or 9 or 16, etc. A simple substitution yields 22x – x² – sqrt x = 114. Omitting the root as the smallest term yields x = 11 ± sqrt 7, i.e 8,35 and 13,65. So two candidates are 9 and 16. I first tried x=9, et voilà... #-)

Dieter