Question

if the centroid of the triangle in which A(a,b) B (b,c) C(c,a) is at the origin the calculate the value of a3 + b3 + c3​

Answer 1

Answer:

it centroid is origin

this implies

the coordinates of centroid is (0,0)

the formula of find centroid is

( (x1+x2+x3)/3 , (y1+y2+y3)/3 )

so

(x1 + x2 + x3)/3 = 0

ATQ

(a + b + c)/3 = 0

a+b+c = 0

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

if we put a + b + c = 0

we get

a³ + b³ + c = 3abc