Question

If the centroid Of ΔABC, in which A(a,b) , B (b,c) and C(c,a) is at origin, then calculate the value of (a³ + b³ + c³)

Answer 1

Here is the answer to your question.



Let A (a, b), B (b, c) and C (c, a) be the vertices of Δ ABC whose medians are AD, BE and CF respectively.

So, D, E and F are the mid points of BC, AC and AB respectively.

∴ Co-ordinates of D are

Centroid G divides median AD in the ratio 2:1 i.e. AG : GD = 2 : 1

∴ co-ordinates of G are



But, it is given that centroid G are (0, 0) ____(2)

Equating (1) & (2)



Now, using identity, if a+b+c = 0, then a3 + b3 + c3 = 3abc.

Answer 2

hello,
the coordinates of the centroid of the triangle are
x=(x₁+x₂+x₃)/3 , y=(y₁+y₂+y₃)/3
so,according to the given question,
(a+b+c)/3=0
a+b+c=0 
we could use the rule/law that if a +b+c =0,
then a³+b³+c³ = 3abc.

bye :-)