help with this multi- variable problem

[perm03]

a) Real numbers x, y, and z are such that xyz > 0 and x+y+z>0. Is it possible that x^2007 + y^2007 + z^2007 < 0?

b) Real numbers v,w,x,y,and z are such that vwxyz > 0 and v+w+x+y+z > 0. Is it possible that v^2007 + w^2007 + x^2007 + y^2007 + z^2007 < 0?

 

[morson]

For the first one, note that x, y and z are all non-zero, and at least one of them is positive, and at least one of them is negative.

Not also that the exponent is odd, and a^x < 0 for a < 0 and x odd

x = -2, y = 4, z = -1 satisfies a

I'm not very well informed in this topic, but I used the above to help. Hope it helped?