Question

If x3 + y3 + z3 = 6xyz and xyz = x + y + z, then the value of (x – y)2 + (y – z)2 + (z – x)2 is equal to

Answer 1

Answer:

Step-by-step explanation:

x3+y3+z3=6xyz—(1)  

x+y+z=xyz—(2)

(1)⟹x3+y3+z3=3xyz+(x+y+z)(x2+y2+z2−xy−yz−zx)=6xyz

⟹(x+y+z)(x2+y2+z2−xy−yz−zx)=3xyz—(3)

Substituting (2) in (3),xyz(x2+y2+z2−xy−yz−zx)=3xyz

⟹x2+y2+z2=3+xy+yz+zx—(4)

(x−y)2+(y−z)2+(z−x)2=2(x2+y2+z2)−2(xy+yz+zx)

=2(3+xy+yz+zx)−2(xy+yz+zx)=6