Question

Tale any values of 'a' ,' b' ,'c' , such that a+b+c=0, and verify a³ + b³ + c³=3 abc​

Answer 1

Step-by-step explanation:

Given: a + b + c = 0

Proof: using algebraic identity,

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

a + b + c = 0

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

so, a³ + b³ + c³ - 3abc = 0 because anything multiplied by 0 is 0

now we shift -3abc to the other side so it changes to positive

therefore, a³ + b³ + c³ = 3abc​

Answer 2

Step-by-step explanation:

Taking a = b = –1 and c = 2

a³ + b³ + c³ = 6

and 3abc = 6 , verified