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If-x-y-2z-k-x-2y-z-k-2x-y-z-k-k-0-then-x-2-y-2-z-2-




Question Number 133612 by benjo_mathlover last updated on 23/Feb/21
If  { ((x+y+2z=k)),((x+2y+z=k)),((2x+y+z=k)) :} ; k≠ 0  then x^2 +y^2 +z^2  =?
$$\mathrm{If}\:\begin{cases}{\mathrm{x}+\mathrm{y}+\mathrm{2z}=\mathrm{k}}\\{\mathrm{x}+\mathrm{2y}+\mathrm{z}=\mathrm{k}}\\{\mathrm{2x}+\mathrm{y}+\mathrm{z}=\mathrm{k}}\end{cases}\:;\:\mathrm{k}\neq\:\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \:=? \\ $$$$ \\ $$
Commented by mr W last updated on 23/Feb/21
x=y=z=(k/4)  x^2 +y^2 +z^2 =((3k^2 )/(16))
$${x}={y}={z}=\frac{{k}}{\mathrm{4}} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\frac{\mathrm{3}{k}^{\mathrm{2}} }{\mathrm{16}} \\ $$
Commented by mr W last updated on 23/Feb/21
why should k≠0?
$${why}\:{should}\:{k}\neq\mathrm{0}? \\ $$

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