>>599
1/x+1/y+1/z=1/a
両辺にxyzをかけると
yz+zx+xy=xyz/a
xy+yz+zx=xyz/a

x^2+y^2+z^2=(x+y+z)^2-2(xy+yz+zx)

x^3+y^3+z^3
=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)+3xyz
=(x+y+z){(x+y+z)^2-3(xy+yz+zx)}+3xyz
=a•(a^2-3xyz/a)+3xyz
=a^3-a•3xyz/a+3xyz
=a^3