Question

 \(\left(x+y+z\right)^2-x^2-y^2-z^2=2\left(xy+yz+zx\right)\)

 Chứng minh đẳng thức trên

Answer 1

(x+y+z)^2-x^2-y^2-z^2=2

=x^2+y^2+z^2+2xy+2yz+2xz-x^2-y^2-z^2

=2xy+2yz+2xz=2(xy+yz+xz) (đpcm)

Answer 2

(x+y+z)²-x²-y²-z²=2(xy+yz+zx)

x²+y²+z²+2xy+2yz+2zx-x²-y²-z²=2(xy+yz+zx)

\(\Rightarrow\)2xy+2yz+2zx=2(xy+yz+zx)

\(\Rightarrow\)2(xy+yz+zx)=2(xy+yz+zx)

vậy (x+y+z)²-x²-y²-z²=2(xy+yz+zx)