SOLUTION: Find two consecutive positive integers such that the sum of their squares is 85.

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Question 18475: Find two consecutive positive integers such that the sum of their squares is 85.
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first positive integer be x
Then the second positive integer will be (x+1)


Given that the sum of their squares is 85,we get:
x^2 + (x+1)^2 = 85
x^2 + x^2 + 1 + 2x = 85
2x^2 + 2x = 85-1
2(x^2+x)=84
2(x^2+x)=2(42)
x^2+x=42
x^2+x-42=0
x^2-6x+7x-42=0
(x-6)(x+7)=0
x=6,-7
We require positive integers hence x cannot be -7
therefore,x=6


first number=6
second number=7


Hope this helps,
Prabhat