Question

Chứng minh rằng:

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

Xin mọi người giúp mink nha, mink đang cần gấp!!!!!

Answer 1

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

\(< =>2x^2+2y^2+2z^2-2xy-2yz-2xz=0\)

\(< =>x^2-2xy+y^2+x^2-2xz+z^2+y^2-2yz+z^2=0\)

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

dấu"=" xảy ra<=>x=y=z

Answer 2

Ta có: \(x^2+y^2+z^2=xy+xz+yz\)

\(\Leftrightarrow2x^2+2y^2+2z^2-2xy-2xz-2yz=0\)

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

\(\Leftrightarrow x=y=z\)