Retarded Algebra

I've been working on this problem in each moment of my spare time for nearly 3 days straight. If I don't figure this shit out, I'll go crazy. I think there's something simple that I'm just not getting.

a + b + c = a^2 + b^2 + c^2 = a^3 + b^3 + c^3 = 3/2.

What is the value of a times b times c?

(%i1) solve([a+b+c=3/2,a^2+b^2+c^2=3/2,a^3+b^3+c^3=3/2],[a,b,c]);
(%o1)
[
[a=(sqrt(6)+2)/4,b=-(sqrt(2)*sqrt(3)-2)/4,c=1/2],
[a=(sqrt(6)+2)/4,b=1/2,c=-(sqrt(2)*sqrt(3)-2)/4],
[a=-(sqrt(6)-2)/4,b=(sqrt(2)*sqrt(3)+2)/4,c=1/2],
[a=-(sqrt(6)-2)/4,b=1/2,c
=(sqrt(2)*sqrt(3)+2)/4],
[a=1/2,b=(sqrt(6)+2)/4,c=-(sqrt(2)*sqrt(3)-2)/4],
[a=1/2,b=-(sqrt(6)-2)/4,c=(sqrt(2)*sqrt(3)+2)/4]
]