(In reply to
Some progress by Brian Smith)
Continuing from where I left off, Multiply each of my two previous equations by abc to get a^2*b+b^2*c+c^2*a = -abc and a^2*c+b^2*a+c^2*b = -abc.
Cube each side of a+b+c=6 and arrange the terms to get (a^3+b^3+c^3) + 3*(a^2*b+b^2*c+c^2*a) + 3*(a^2*c+b^2*a+c^2*b) + 6*abc = 216.
Now substitute the prior equations into the last equation to yield (a^3+b^3+c^3) + 3*(-abc) + 3*(-abd) + 6*abc = 216, which simplifies to a^3+b^3+c^3 = 216.
re: Some progress - Solution
