the 3 consecutive integers can be written as:

x-1, x and x+1, where x is integer

the square of the sum of the lesser two is equal to twice the greatest

(x-1 + x)^2 = 2(x + 1)

by solving we find:

x1 = 1.65

x2 = -0.15

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since the solutions are not integers we conclude that there are no such 3 consecutive integers.