Chứng minh,thực hiện phép tính

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harrydo

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transformers123

$x^2+y^2+z^2=xy+xz+yz$

$\iff 2x^2+2y^2+2z^2=2xy+2yz+2zx$

$\iff (x-y)^2+(y-z)^2+(z-x)^2=0$

Mà $(x-y)^2+(y-z)^2+(z-x)^2 \ge 0$

Nên $(x-y)^2+(y-z)^2+(z-x)^2=0$ khi:

$\begin{cases}x-y=0\\y-z=0\\z-x=0\end{cases} \iff \begin{cases}x=y\\y=z\\z=x\end{cases} \iff x=y=z\ (\mathfrak{Dpcm})$
 
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