Question

If a+b+c= 0 . then find a^2/bc+b^2/ca+c^2/ab​

Answer 1

Answer:

3

Step-by-step explanation:

Given---> If a + b + c = 0

To find---> a²/bc + b²/ca + c²/ab

Solution---> ATQ,

a + b + c = 0

a³+b³+c³-3abc =(a+b+c) (a² + b² + c² - ab - bc - ca )

Now putting , a + b + c = 0 in it , we get,

=> a³+b³+c³ - 3abc = ( 0 ) ( a²+b²+c²-ab-bc-ca )

=> a³ + b³ + c³ - 3abc = 0

=> a³ + b³ + c³ = 3abc

Now returning to original problem , we get,

a² / bc + b² / ca + c² / ab

Taking abc , LCM , we get,

= ( a³ + b³ + c³ ) / abc

Now putting ( a³ + b³ + c³ ) = 3abc , we get,

= 3 abc / abc

abc cancel out from numerator and denominator and we get,

= 3

Additional identities--->

1) a² - b² = ( a + b ) ( a - b )

2) ( a + b )² = a² + b² + 2ab

3) ( a - b )² = a² + b² - 2ab

4) ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

5) ( a + b )³ = a³ + b³ + 3ab ( a + b )

6) ( a - b )³ = a³ - b³ - 3ab ( a - b )

#Answerwithquality&BAL

Answer 2

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3

#answerwithquality #bal