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transformers123

$ax+by+cz=(x^2-yz)x+(y^2-xz)y+(z^2-xy)z$

$\iff ax+by+cz=x^3+y^3+z^3-3xyz$

$\iff ax+by+cz=(x+y)^3+z^3-3xy(x+y)-3xyz$

$\iff ax+by+cz=(x+y+z)[(x+y)^2-(x+y)z+z^2]-3xy(x+y+z)$

$\iff ax+by+cz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)$

Mà $a+b+c=x^2+y^2+z^2-xy-yz-zx$

Nên $(x+y+z)(x^2+y^2+z^2-xy-yz-zx)\ \vdots\ (a+b+c)$

Vậy $(ax+by+cz)\ \vdots\ (a+b+c)$
 
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