Answer:
3, 4, 5
Step-by-step explanation:
I like to let x represent the middle integer. Then the first is x-1 and the third is x+1. The given relation is ...
(x-1)^2 +2x = 4(x+1) -3
We can put this equation into standard form and solve.
x^2 -2x +1 +2x = 4x +4 -3
x^2 -4x = 0 . . . . . subtract 4x+1
x(x -4) = 0
So, x=0 is a solution to the equation, but an extraneous solution with respect to the problem.
x = 4 is also a solution to the equation, indicating the integers are 3, 4, 5.
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Check
3^2 +2·4 = 4·5 -3
17 = 17 . . . . answer checks OK
