SOLUTION: what are 2 consecutive positive intergers such that the sum of their squares is 85?

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Question 59539: what are 2 consecutive positive intergers such that the sum of their squares is 85?
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
x and x+1 are the integers
+x%5E2+%2B+%28x%2B1%29%5E2+=+85+
foil the binomial
+x%5E2+%2B+x%5E2+%2B+2x+%2B+1+=+85+
combine like terms
+2x%5E2+%2B+2x+%2B1+=+85+
subtract 85 from both sides
+2x%5E2+%2B+2x+-+84+=+0+
divide all parts by 2
+x%5E2+%2B+x+-42+=+0+
factor
+%28x%2B7%29%28x-6%29=0+
set each part equal to zero
+x%2B7+=+0+ and +x-6=0+
+x=-7+ and +x=6+
The stipulation calls for only POSITIVE numbers
+x=6+
so ... +x%2B1+=+7+

CHECK
+6%5E2+%2B+7%5E2+=+85+
+36+%2B+49+=+85+
+85+=+85+
TRUE!!!