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