Ta có:
\(VT=3\left(x^2+y^2+z^2\right)-\left(x-y\right)^2-\left(z-x\right)^2-\left(y-z\right)^2\)
\(=3x^2+3y^2+3z^2-\left(x^2-2xy+y^2\right)-\left(z^2-2xz+x^2\right)-\left(y^2-2yz+z^2\right)\)
\(=3x^2+3y^2+3z^2-x^2+2xy-y^2-z^2+2xz-x^2-y^2+2yz-z^2\)
\(=x^2+y^2+z^2+2xy+2xz+2yz\)
\(=\left(x+y+z\right)^2=VP\)
⇒ Đpcm
\(3\left(x^2+y^2+z^2\right)-\left(x-y\right)^2-\left(z-x\right)^2\)
\(=3\left(x^2+y^2+z^2\right)-\left(x^2-2xy+y^2\right)-\left(z^2-2xz+x^2\right)\)
\(=3x^2+3y^2+3z^2-x^2+2xy-y^2-z^2+2xz-x^2\)
\(=x^2+2y^2+2z^2+2xy+2xz\)
Mà: \(\left(x+y+z\right)^2=x^2+y^2+z^2+2xy+2yz+2xz\)
Mong bạn kiểm tra lại đề bài!
