Posted by Janice - Please Help!!! on Tuesday, June 7, 2011 at 4:12pm.
The property translates to the following equation:
x^3-(x-1)^3-(x-2)^3-(x-3)^3=0
Expanding:
-2x^3+18x^2-42x+36 = 0
2(-x³+9x²-24x+18)=0
which factorizes to:
-2(x-6)(x^2-3x+3)=0
or simply:
(x-6)(x^2-3x+3)=0
The first factor gives x=6 (our answer), and the second factor is not further factorizable.
Attempts to solve
(x^2-3x+3)=0
results in a complex number, so no other real roots exist.
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