express in terms of elementary symmetric functions. Let

\(\displaystyle x+y+z=s\)

\(\displaystyle x y + y z + z x = r\)

\(\displaystyle x y z=p\)

we get

\(\displaystyle x^2+y^2+z^2=s^2-2r=2\)

\(\displaystyle x^3+y^3+z^3=3p+s^3-3s r=3\)

since \(\displaystyle s=1\) the above equations give \(\displaystyle r=-1/2, p= 1/6\)

therefore

\(\displaystyle x^4+y^4+z^4=4p s+s^4-4s^2r+2r^2=\frac{25}{6}\)