Hi

Let x and (x+1) represent the two consecutive integers

Question states***

 [x + (x+1)]^2 = 81

Solving for x

 (2x+1)^2 = 81

 4x^2 + 4x + 1 = 81

 4x^2 + 4x -80 = 0

 x^2 + x -20 = 0

factoring

(x+5)(x-4) = 0

(x+5)= 0   x = -5    the two consecutive integers are -5,-4

or

(x-4) = 0  x = 4     the two consecutive integers are 4,5

 

CHECKING our Answer***

 (-9)^2 = 81

 (9)^2= 81 

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