SOLUTION: two numbers differ by 8 and the sum of their squares is 320. find the two numbers

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Question 259570: two numbers differ by 8 and the sum of their squares is 320. find the two numbers
Answer by drk(1908) About Me  (Show Source):
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Let X and Y be the numbers. We get
(i) x-y+=+8
(ii) x%5E2%2By%5E2+=+320
solve (i) for x to get
(iii) x+=+8+%2B+y
substitute (iii) into (ii) to get
(iv) %288%2By%29%5E2+%2B+y%5E2+=+320
expanding, we get
(v) y%5E2+%2B+16y+%2B+64+%2B+y%5E2+=+320
combine like terms to get
(vi) 2y%5E2+%2B+16y+%2B+64+=+320
setting =0 and factoring, we get
(vii) 2y%5E2+%2B+16y+-256+=+0
factored, we get
(viii) %28y%2B16%29%28y-8%29=0
solving for y, we get
y = -16 or y = 8.
So, we have (-8, -16) ; (16,8)