Question 470907
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Hi,
Let x and (x+1) represent the two consecutive positive integers
Question states***
 x^2 + (x+1)^2 = 8x + 9
x^2 + x^2 + 2x + 1 = 8x +9
   2x^2 -6x - 8 = 0
    x^2 - 3x - 4 = 0
factoring
   (x-4)(x+1) = 0
   (x-4) = 0   x = 4    Integers are 4,5
   (x+1) = 0   x = -1  Toss out, looking for positive pair

CHECKING our Answer***
  16 + 25 = 41 = 32+9