Finding the min value

**RuyHayabusa** · March 3rd 2013, 02:54 AM

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.

**a tutor** · March 3rd 2013, 04:32 AM

That's not number theory.

It amounts to figuring out what point in the plane x+y+z=1 is closest to the origin.

**Nehushtan** · March 3rd 2013, 07:06 AM

$\begin{array}{rcl} \left(x-\dfrac13\right)^2+\left(y-\dfrac13\right)^2+\left(z-\dfrac13\right)^2 & \geqslant & 0 \\\\ x^2+y^2+z^2 & \geqslant & \dfrac23(x+y+z)-3\left(\dfrac19\right) \\\\ {} & = & \dfrac13 \end{array}$

**davidrussel** · March 15th 2013, 09:19 PM

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