Question

18. If a2 + b2 + c2 = ab + bc + ca , then the value
of a + b3 + c' is​

Answer 1

Textbook Solutions

Schools & Teachers

Content Guidelines

Honor code

Community

amitktyagi15 avatar

amitktyagi15

12.01.2020

Math

Secondary School

answered

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

2

SEE ANSWERS

Answer

3.0/5

3

upadanrtm2020

Virtuoso

110 answers

6.6K people helped

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 .

Explanation:

Hope you have satisfied with this answer.So please follow me and thank me and make me as brainlesset soon and vote my answer.