Question

Tìm x,y,z biết:

\(x^2+y^2+z^2=xy+yz+xz\)và \(x^{2009}+y^{2009}+z^{2009}=3^{2010}\)

Answer 1

\(x^2+y^2+z^2=xy+yz+xz\)

\(\Leftrightarrow2x^2+2y^2+2z^2=2xy+2yz+2xz\)

\(\Leftrightarrow\left(x^2+y^2-2xy\right)+\left(y^2+z^2-2yz\right)+\left(x^2+z^2-2xz\right)=0\)

\(\Leftrightarrow\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2=0\)

\(\Leftrightarrow.....\)

Answer 2

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