Question

104. If a2 +b2 +c2 = ab + bc + ca then the
value of a3 + b3 + c3 is:
(A) 3abc
(B) 3(abc)3
(C) 3a2b2c2
(D) None of these​

Answer 1

Application of Algebraic Identity

Answer: when a² + b² + c² =  ab + bc + ca  , a³ + b³ + c³ = 3abc and correct option is (A) 3abc .

Explanation:

Given that a² + b² + c² = ab + bc + ca .

Need to find the value of a³ + b³ + c³

This is straight application of following algebraic identity

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

on modifying above identity as

a³ + b³ + c³ - 3abc = ( a + b + c ) ( a² + b² + c² - ( ab + bc + ca ) )   ------ eq(1)

As given that  a² + b² + c² =  ab + bc + ca

=> a² + b² + c² - ( ab + bc + ca ) = 0

so on substituting a² + b² + c² - ( ab + bc + ca ) = 0 in eq(1) , we get

a³ + b³ + c³ - 3abc = ( a + b + c ) × ( 0 )

=> a³ + b³ + c³ - 3abc = 0

=> a³ + b³ + c³ = 3abc

Hence when a² + b² + c² =  ab + bc + ca  , a³ + b³ + c³ = 3abc and correct option is (A) 3abc .

#answerwithquality

#BAL

Answer 2

Answer:

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