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The difference of two numbers is 6 and the sum of their squares is 68. Find the numbers.

 Feb 22, 2020
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The difference of two numbers is 6 and the sum of their squares is 68. Find the numbers. 

 

X –  Y  =  6 

X2 + Y2  =  68 

 

Without doing lengthy calculations, I recognized that the larger number has to be 8 or less.

 

So I said, 64 and what equals 68 and the answer was 4.  The sqrt(4) is 2. 

 

8 – 2  =  6  so I happened to get it right on the first try.  The numbers are 8 and 2

 

If 8 hadn't worked I'd have tried 7.  49 and what equals 68, the answer is 19. 

19 isn't a perfect square so this pair fails.  Moving on to 6.  36 and 32 don't work. 

nor do 25 and 43,  nor do 16 and 52.  nor 9 and 59. 

the next one to try is 4 and we already know that 2 is one of the numbers.  We're done. 

.

 Feb 22, 2020

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