Câu hỏi của Thanh Tu Nguyen

Question

Cho $x^2+y^2+z^2=xy+yz+zx$ Chứng minh rằng x=y=z

Nguyễn Gia Khánh · Accepted Answer

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

=> $2x^2+2y^2+2x^2=2xy+2yz+2zx$

=> $2x^2+2y^2+2x^2-2xy-2yz-2zx=0$

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

=> x -y =0 ; y - z=0 ; z - x=0

=> x =y; y =z; z=x

=> x=y=zCâu trả lời: $x^2+y^2+z^2=xy+yz+zx$

=> $2x^2+2y^2+2x^2=2xy+2yz+2zx$

=> $2x^2+2y^2+2x^2-2xy-2yz-2zx=0$

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

=> x -y =0 ; y - z=0 ; z - x=0

=> x =y; y =z; z=x

=> x=y=z