Question 1196609
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For a purely mental solution, you can reason that, since the two ages are close together, the squares of the ages are relatively close together.<br>
So divide the sum of the squares of their ages, 520, by 2 to get 260, then observe that a perfect square close to 260 is 16^2 = 256; so very likely the two ages (since they are 4 apart) are 16+2=18 and 16-2=14.<br>
Check to see if that works....<br>
18^2+14^2 = 324+196 = 520<br>
ANSWERS: 14 and 18<br>