SOLUTION: The sum of two integers is 10, and the sum of their squares is 250. Find the two integers. Only an algebraic solution will be accepted.

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Question 1102793: The sum of two integers is 10, and the sum of their squares is 250. Find the two integers. Only an algebraic solution will be accepted.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +x+%2B+y+=+10+
(2) +x%5E2+%2B+y%5E2+=+250+
--------------------------
(1) +y+=+10+-+x+
and
(2) +x%5E2+%2B+%28+10+-+x+%29%5E2+=+250+
(2) +x%5E2+%2B+100+-+20x+%2B+x%5E2+=+250+
(2) +2x%5E2+-+20x+-+150+=+0+
(2) +x%5E2+-+10x+-+75+=+0+
(2) +%28+x+-+15+%29%2A%28+x+%2B+5+%29+=+0+ ( by looking at it )
+x+-+15+=+0+
+x+=+15+
and
(1) +x+%2B+y+=+10+
(1) +15+%2B+y+=+10+
(1) +y+=+-5+
-----------------------
(2) +x%5E2+%2B+y%5E2+=+250+
(2) +15%5E2+%2B+%28-5%29%5E2+=+250+
(2) +225+%2B+25+=+250+
(2) +250+=+250+
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The integers are 15 and -5