Thread: number theory

1) Find the minimum value of (x^2)+(y^2)+(z^2)/2,such that x+y+z=10.
2) If x+y+z=2, (x^2)+(y^2)+(z^2)=4, show that (x^3)+(y^3)+(z^3)> or =8

Are there any restrictions on ? (Do they have to be integers?) If not, you can just use Lagrange Multipliers.