Setting a, b, and c is really smart.
a = 3x
b = 5y
c = -6z
3x + 5y - 6z = 2
a + b + c = 2
5xy - 10yz - 6xz = -41
ab + bc + ac = -123
xyz = 6
abc = -540
x^3 - 2x^2 - 123x + 540
(x - 5)(x - 9)(x + 12) # I don't know how to factor cubic equations, I just plugged it into a calculator.
x = 5, 9, -12
a = 3x
b = 5y
c = -6z
a = 5, b = 9
5/3 + 9/5 = 52/15
a = 5, b = -12
5/3 - 12/5 = -11/15
a = 9, b = 5
9/3 + 5/5 = 4
a = 9, b = -12
9/3 - 12/5 = 3/5
a = -12, b = 5
-12/3 + 5/5 = -3
a = -12, b = 9
-12/3 + 9/5 = -11/5
Everything looks right to me, I'm not sure why it's wrong. :((
Looking at Asinus's answer from the link guest sent, he had the same aproach too.
=^._.^=