Question

If x = b + c, y = c + a and z = a+b then find the value of x 2 + y 2 + z 2 - yz - zx - xy/ a 2 + b 2 + c 2 - bc - ca - ab

Answer 1

Given, x−y=(b+c)−(c+a)=b−a

Similarly y−z=c−b and z−x=a−c

Now x2+y2+z2−yz−zx−xy

=21[(x−y)2+(y−z)2+(z−x)2]

=21[(b−a)2+(c−b)2+(a−c)2]

=21[(a−b)2+(b−c)2+(c−a)2]

a2+b2+c2−bc−ca−ab