Question

very fy that question 12 plz​

Answer 1

We know that ;

$x^3+y^3+z^3-3xyz =(x+y+z)(x^2+y^2+z^2-xy-yz-zx)$

Multiplying RHS by 2 and dividing RHS by 2 we get ;

$=\frac{1}{2}*2 (x+y+z)(x^2+y^2+z^2-xy-yz-zx)\\\\=\frac{1}{2}*2 (x+y+z)(2x^2+2y^2+2z^2-2xy-2yz-2zx)\\\\=\frac{1}{2}*2 (x+y+z)((x^2-2xy+y^2)+(y^2-2yz+z^2)+(z^2-2zx+x^2))\\\\=\frac{1}{2}*2 (x+y+z)((x-y)^2+(y-z)^2+(z-x)^2)$

Hence, proved.