Question

if a3+b3+c3=3abc then find a+b+c=?

Answer 1

if a3+b3+c3 = 3abc then a+b+c= 0

Answer 2

Heya......!!!!


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

Now it is given that : a3 + b3 + c3 = 3abc

So,

=> a3 + b3 + c3 - 3abc = 0
=> (a + b + c )(a2 + b2 + c2 -ab - ac -bc) = 0
that is =>>>
(a2 + b2 + c2 -ab - ac -bc) = 0 or (a + b + c ) = 0

(a2 + b2 + c2 -ab - ac -bc) = 0 cannot be zero because:
2a² + 2b² + 2c² -2ab - 2ac - 2bc = 0 
a² + b² -2ab + a² +b² +2c² - 2ac -2bc = 0 
(a-b)² + a² + c² -2ac + b² + c² -2bc = 0 
(a-b)² + (a-c)² + (b-c)² = 0

As a≠b≠c SO ,,, a+b+c = 0



HOPE IT HELPS U