Question 60835: Can someone please help me figure this out?
Find two consecutive positive integers such that the sum of their squares is 85.
Answer by jai_kos(139)   (Show Source):
You can put this solution on YOUR website! Let the two consecutive integer be x and x +1
Sum of their squares is 85.
That means
x^2 +( x +1)^2 = 85
x^2 +x^2 + 1 + 2x = 85
2x^2 +2x = 85 -1
2x^2 + 2x = 84
2x^2 + 2x -84 =0
Divide the above equation by 2, we get
x^2 +x - 42 = 0
x^2 + 7x -6x – 42 =0
x(x +7) – 6 (x +7) = 0
(x - 6) (x + 7) = 0
x - 6 = 0 or x + 7 = 0
x = 6 or -7
So when x = 6, we get (x+1) = 6 +1 = 7
So when x =-7, (x +1) = - 7 + 1 = - 6
Therefore the consecutive numbers are 6,7 and -7 , 6
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