Question

2a​2+2b2+2c2​-2ab-2bc-2ca = (a-b)2​+(b-c)2​+(c-a)2​ Prove it ​ ​​​​​​​​​

Answer 1

Answer:

12

Step-by-step explanation:

Answer 2

To prove :

2a² + 2b² + 2c²- 2ab - 2bc -2ca = [ (a-b)^2 + (b-c)^2 + (c-a)^2 ]

Proof :

L.H.S = 2a² + 2b² + 2c² - 2ab - 2bc - 2ca

a² + a² + b² + b² + c² + c² - 2ab - 2bc - 2ca

a² - 2ab + b² + b² - 2bc + c² + c² - 2ca + a²

( a² - 2ab + b² ) +( b² - 2bc + c² )+ ( c² - 2ca + a² )

Using ( a - b )² = a² - 2ab + b² ,

( b - c )² = b² - 2bc + c² ,

( c - a )² = c² - 2ac + a²

L.H.S = ( a - b )² + ( b - c )² + ( c - a )²

L.H.S = R.H.S

( a - b )² + ( b - c )² + ( c - a )² = ( a - b )² + ( b - c)² + ( c - a )²

Hence Proved.