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Thread: number theory

  1. #1
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    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
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  2. #2
    Senior Member roninpro's Avatar
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    Are there any restrictions on $\displaystyle x,y,z$? (Do they have to be integers?) If not, you can just use Lagrange Multipliers.
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