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Question-167839




Question Number 167839 by mathlove last updated on 27/Mar/22
Answered by mr W last updated on 27/Mar/22
say x+y+z−3=s   ⇒x+y+z−s=3   [((1/(668)),(1/(669)),(1/(670)),0),((1/(670)),(1/(671)),(1/(672)),0),((1/(674)),(1/(675)),(1/(676)),0),(1,1,1,(−1)) ] ((x),(y),(z),(s) )= ((1),(1),(1),(3) )  s= [((1/(668)),(1/(669)),(1/(670)),1),((1/(670)),(1/(671)),(1/(672)),1),((1/(674)),(1/(675)),(1/(676)),1),(1,1,1,3) ]/ [((1/(668)),(1/(669)),(1/(670)),0),((1/(670)),(1/(671)),(1/(672)),0),((1/(674)),(1/(675)),(1/(676)),0),(1,1,1,(−1)) ]=2012
$${say}\:{x}+{y}+{z}−\mathrm{3}={s}\: \\ $$$$\Rightarrow{x}+{y}+{z}−{s}=\mathrm{3} \\ $$$$\begin{bmatrix}{\frac{\mathrm{1}}{\mathrm{668}}}&{\frac{\mathrm{1}}{\mathrm{669}}}&{\frac{\mathrm{1}}{\mathrm{670}}}&{\mathrm{0}}\\{\frac{\mathrm{1}}{\mathrm{670}}}&{\frac{\mathrm{1}}{\mathrm{671}}}&{\frac{\mathrm{1}}{\mathrm{672}}}&{\mathrm{0}}\\{\frac{\mathrm{1}}{\mathrm{674}}}&{\frac{\mathrm{1}}{\mathrm{675}}}&{\frac{\mathrm{1}}{\mathrm{676}}}&{\mathrm{0}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{−\mathrm{1}}\end{bmatrix}\begin{pmatrix}{{x}}\\{{y}}\\{{z}}\\{{s}}\end{pmatrix}=\begin{pmatrix}{\mathrm{1}}\\{\mathrm{1}}\\{\mathrm{1}}\\{\mathrm{3}}\end{pmatrix} \\ $$$${s}=\begin{bmatrix}{\frac{\mathrm{1}}{\mathrm{668}}}&{\frac{\mathrm{1}}{\mathrm{669}}}&{\frac{\mathrm{1}}{\mathrm{670}}}&{\mathrm{1}}\\{\frac{\mathrm{1}}{\mathrm{670}}}&{\frac{\mathrm{1}}{\mathrm{671}}}&{\frac{\mathrm{1}}{\mathrm{672}}}&{\mathrm{1}}\\{\frac{\mathrm{1}}{\mathrm{674}}}&{\frac{\mathrm{1}}{\mathrm{675}}}&{\frac{\mathrm{1}}{\mathrm{676}}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{3}}\end{bmatrix}/\begin{bmatrix}{\frac{\mathrm{1}}{\mathrm{668}}}&{\frac{\mathrm{1}}{\mathrm{669}}}&{\frac{\mathrm{1}}{\mathrm{670}}}&{\mathrm{0}}\\{\frac{\mathrm{1}}{\mathrm{670}}}&{\frac{\mathrm{1}}{\mathrm{671}}}&{\frac{\mathrm{1}}{\mathrm{672}}}&{\mathrm{0}}\\{\frac{\mathrm{1}}{\mathrm{674}}}&{\frac{\mathrm{1}}{\mathrm{675}}}&{\frac{\mathrm{1}}{\mathrm{676}}}&{\mathrm{0}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{−\mathrm{1}}\end{bmatrix}=\mathrm{2012} \\ $$

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