Question

Prove that : (a2 - b2) 3 + (b2 - c 2) 3 + (c2 - a 2) 3 = 3 (a2- b2)(b2- c 2)(c2- a 2)​

Answer 1

Answer :

Prove that : ( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³ = 3( a² - b² )( b² - c² )( c² - a² )

Let's recall one identity, if x + y + z = 0 then x³ + y³ + z³ = 3xyz

And now let's solve accordingly

First check the condition x + y + z = 0

( a² - b² ) + ( b² - c² ) + ( c² - a² ) = 0

Therefore by the identity : x³ + y³ + z³ = 3xyz

( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³ = 3( a² - b² )( b² - c² )( c² - a² )

Hence proved