Question

If a+b+c is not equal to zero then prove that a³+b³+c³=3abc only when a=b=c.

Answer 1

Step-by-step explanation:

anjalirocks679 here is your answer!

We know,

a

3

+b

3

+c

3

−3abc=(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)

Putting a+b+c=0 on RHS, we get,

a

3

+b

3

+c

3

−3abc=0

⟹a

3

+b

3

+c

3

=3abc, Hence proved

Answer 2

$\sf{SOLUTION:-}$

☆ a³ + b ³ + c ³ - 3abc = ( a + b + c ) (a²+ b ² + c² - ab - bc - ca )

On putting ;

a + b + c = 0 {On R.H.S. We get a³ + b³ + c³ - 3abc = 0}

» a³ + b³ + c³ = 3abc

$\huge\fbox\red{Hence\:Proved\:}$