9514 1404 393
Answer:
9, 10 or -10, -9
Explanation:
Let x represent the smaller of the two numbers. Then x+1 is the larger, and their difference is ...
(x +1)³ -x³ = 271
x³ +3x² +3x +1 -x³ = 271
3x² +3x -270 = 0 . . . . . . simplify
x² +x -90 = 0 . . . . . . . . divide by 3
(x +10)(x -9) = 0 . . . . . factor
The two solutions are x = -10, x = 9.
The numbers could be {-10, -9} or {9, 10}.
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Additional comment
Solutions to a factored polynomial are the values of the variable that make the factors zero. The product will only be zero if a factor is zero.
The factor (x -a) is zero when x=a.