Question

If x=(a - b) y =(b-c),z=(c-a) then x +y +z = + 2​

Answer 1

Given x=b-c ,y=c-a and z=a-b

Then x

2

−y

2

+z

2

+2xz

=(b−c)

2

−(c−a)

2

+(a−b)

2

+2(b−c)(a−b)=b

2

−2bc+c

2

−c

2

−a

2

+2ac+a

2

+b

2

−2ab+2ab−2ac−b

2

+2bc=0

Answer 2

Answer:

x = a - b

y = b - c

z = c - a

x+y+z=a−b+b−c+c−a=0

Therefore, x3+y3+z3−3xyz=(x+y+z)

= 0