# Finding the min value

• Mar 3rd 2013, 02:54 AM
RuyHayabusa
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.
• Mar 3rd 2013, 04:32 AM
a tutor
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.
• Mar 3rd 2013, 07:06 AM
Nehushtan
Re: Finding the min value
$\begin{array}{rcl} \left(x-\dfrac13\right)^2+\left(y-\dfrac13\right)^2+\left(z-\dfrac13\right)^2 & \geqslant & 0 \\\\ x^2+y^2+z^2 & \geqslant & \dfrac23(x+y+z)-3\left(\dfrac19\right) \\\\ {} & = & \dfrac13 \end{array}$
• Mar 15th 2013, 09:19 PM
davidrussel
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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