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Math Help - Finding the min value

  1. #1
    Junior Member
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    Finding the min value

    Hey everyone,

    I need some help on finding the min value of x^2+y^2+z^2 if x + y + z is 1

    Thanks.
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  2. #2
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    Re: Finding the min value

    That's not number theory.

    It amounts to figuring out what point in the plane x+y+z=1 is closest to the origin.
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  3. #3
    Junior Member Nehushtan's Avatar
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    Re: Finding the min value

    \begin{array}{rcl} \left(x-\dfrac13\right)^2+\left(y-\dfrac13\right)^2+\left(z-\dfrac13\right)^2 & \geqslant & 0 \\\\ x^2+y^2+z^2 & \geqslant & \dfrac23(x+y+z)-3\left(\dfrac19\right) \\\\ {} & = & \dfrac13 \end{array}
    Thanks from RuyHayabusa
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  4. #4
    Newbie davidrussel's Avatar
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    Re: Finding the min value

    The formula given above sees correct for the problem asked. this has calculated the exact amount of min value.
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