Question

pplz someone answer fast i asked previously but no one answered

Answer 1

We know,--->.

if a + b + c = 0 ;

a³ + b³ + c³ = 3abc

We observe,

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

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

= 3( a² - b² )( b² - c² )( c² - a² )

=3(a-b)(a+b)(b-c)(b+c)(c-a)(c+a)

Similarly,

( a - b ) + ( b - c ) + ( c - a ) = 0

=> ( a - b )³ + ( b - c )³ + ( c - a )³

= 3( a - b )( b - c )( c - a )

Now,

= [ ( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³ ] / [ ( a - b )³ + ( b - c )³ + ( c - a )³ ]

= 3( a² - b² )( b² - c² )( c² - a² ) / 3( a - b )( b - c )( c - a )

=3(a-b)(a+b)(b-c)(b+c)(c-a)(c+a)/3( a - b )( b - c )( c - a )

= ( a + b )( b + c )( c + a ) <---- Answer..

I HOPE THIS WILL HELP YOU