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

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- Feb 6th 2011, 04:01 PMchris86number 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 - Feb 6th 2011, 05:39 PMroninpro
Are there any restrictions on $\displaystyle x,y,z$? (Do they have to be integers?) If not, you can just use Lagrange Multipliers.