Question

If the centroid of a triangle formed by the points (a,b),(b,c),(c,a) is At origin then a³+b³+c³=???

Answer 1

If the vertices of the ∆ABC be A(a,b) ; B(b,c) ; C(c,a)

Then the coordinates of the centroid will be

P(x,y)= {(a+b+c)/3, (a+b+c)/3};P(x,y)=(0,0)…….. (given)

=> (a+b+c)=0

Using identity

a^3+b^3+c^3–3abc= (a+b+c)(a^2+b^2+c^2-ab-bc-ca)a^3+b^3+c^3–3abc=0a^3+b^3+c^3=3abc