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$(\sum \left | x+y-z \right |) + \left | x+y+z \right | \geqslant 2(\sum \left | x \right |)$


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#1
RoyalMadrid

RoyalMadrid

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Chứng minh rằng với mọi số thực x,y,z:

$\left | x+y-z \right |+\left | y+z-x \right |+\left | x+z-y \right | \left +| x+y+z \right | \geqslant 2(\left | x \right |+\left | y \right |+\left | z \right |)$

Dấu "=" xảy ra khi nào?






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