Question

answer pls answer all of them i will mark you as a brainliest

Answer 1

Given,

⇒ a + b + c = 0

To prove : ( a²/bc ) + ( b²/ca ) + ( c²/ba ) = 3

Proof :

⇒ ( a²/bc ) + ( b²/ca ) + ( c²/ba ) = 3

⇒ ( a³ + b³ + c³ ) / abc = 3

We know that, if ( a + b + c ) = 0

Then,

⇒ ( a³ + b³ + c³ ) = 3abc

⇒ 3abc / abc = 3

•°• 3 = 3

Proved !!

Proof of identity used in this solution :

Given,

⇒ a + b + c = 0

⇒ a + b = -c --------- ( 1 )

Cubing both sides,

⇒ ( a + b )³ = ( -c )³

⇒ a³ + b³ + 3ab( a + b ) = -c³

Substitute the value of ( 1 ),

⇒ a³ + b³ + 3ab( -c ) = -c³

⇒ a³ + b³ - 3abc = -c³

•°• a³ + b³ + c³ = 3abc