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

Guest Feb 22, 2020

#1**0 **

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

X – Y = 6

X^{2} + Y^{2} = 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.

_{.}

Guest Feb 22, 2020