SOLUTION: The sum of the squares of two consecutive, positive integers is 85. Find the integers.
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Question 112524: The sum of the squares of two consecutive, positive integers is 85. Find the integers.
Found 2 solutions by checkley71, ilana:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
X^2+(X+1)^2=85
X^2+X^2+2X+1-85=0
2X^2+2X-84=0
(2X-12)(X+7)=0
2X-12=0
2X=12
X=12/2
X=6 ANSWER FOR THE FIRST INTEGER.
6+1=7 FOR THE SECOND INTEGER.
PROOF
6^2+7^2=85
36+49=85
85=85
Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
We could call any two consecutive integers x and x+1, so we will solve for the smaller integer. So we know x^2 + (x+1)^2 = 85. Now expand the terms to get x^2 + x^2 + 2x + 1 = 85. Simplify to get 2x^2 + 2x - 84 = 0. Factor this to get x=6 and x=-7. So the consecutive positive integers are 6,7.
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