Question

CMR: x²+y²+z²-xy-yz-xz=\(\frac{\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2}{2}\)

Answer 1

Ta có : \(x^2+y^2+z^2-xy-yz-zx\)

\(=\frac{1}{2}.\left(2x^2+2y^2+2z^2-2xy-2yz-2zx\right)\)

\(=\frac{\left(x^2-2xy+y^2\right)+\left(y^2-2yz+z^2\right)+\left(z^2-2xz+x^2\right)}{2}\)

\(=\frac{\left(x-y\right)+\left(y-z\right)^2+\left(z-x\right)^2}{2}\) ( đpcm )