SOLUTION: One number exceeds another by 5.The sum of their squares is 157.What are the numbers?

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Question 701482: One number exceeds another by 5.The sum of their squares is 157.What are the numbers?
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
Let +N+ be one of the numbers


"One number exceeds another by 5":
then the other is +N%2B5+


"The sum of their squares is 157":
+N%5E2+%2B+%28N%2B5%29%5E2+=+157+
+N%5E2+%2B+N%5E2+%2B+10N+%2B+25+=+157+
+2N%5E2+%2B+10N+-132+=+0+
+N%5E2+%2B+5N+-66+=+0+
+%28N-6%29%28N%2B11%29+=+0+
This quadratic has two solutions: +N=6+ and +N=-11+

Consider N=6:
1st number=N=6, 2nd number=N+5=11

Consider N=-11:
1st number=N=-11, 2nd number=N+5=-6