Question

Verify the a2+b2+c2.3abc=1/2 (a+b+c).(a-b)2+(b-c)2+(c-a)2.​

Answer 1

Step-by-step explanation:

LHS-

(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)

⟹a(a

2

+b

2

+c

2

−ab−bc−ca)+b(a

2

+b

2

+c

2

−ab−bc−ca)+c(a

2

+b

2

+c

2

−ab−bc−ca)

=a

3

+ab

2

+ac

2

−a

2

b−abc−a

2

c+ba

2

+b

3

+bc

2

−b

2

a−b

2

c−bca+ca

2

+cb

2

+c

3

−cab−c

2

b−c

2

a

=a

2

+b

2

+c

2

−3abc