Given:
x+y+z=1 x^{2}+y^{2}+z^{2}=2x^{4}+y^{4}+z^{4}=4
Find:x^{3}+y^{3}+z^{3} Attempt at Solving:Note: x^{3}+y^{3}+z^{3}-3xyz=(x+y+z)(x^{2}+y^{2}+z^{2}-xy-xz-yz)(x+y+z)^{2}=x^{2}+y^{2}+z^{2}+2xy+2xz+2zy=1xy+xz+zy=-1/2 Plugging in the unknown, we get:x^{3}+y^{3}+z^{3}-3xyz=(1)(2-(-1/2)) Now I...