Question

the centroid formedof a triangle formed by the poits A(a,b),(b,c),(c,a) is at origin then acube +bcube+ccube

Answer 1

Triangle is formed by  points : A (a, b)   ,  B(b , c)    C (c , a)
Centroid :  O : x = (a+b+c)/3          y = (b+c+a)/3

   hence,  a+b+c = 0
     so  a + b = - c
   cube on both sides
               a³ + b³ + 3 a b ( a + b) = - c³
               a³ + b³ + c³ = 3 a b (-c)  = - 3 a b c