If the centroid of a triangle is formed by the points (a,b), (b,c) and (c,a) is at the origin i.e. (0,0) then a^3 + b^3 + c^3 = ??
3abc
Centroid x coordinate = (a + b + c)/3 = 0 Therefore a + b + c = 0
Now, a^3 + b^3 + c^3 -3abc = (a + b + c)(a^2 + ..... + c2) = 0, as (a + b + c) = 0
Therefore a^3 + b^3 + c^3 = 3abc
If, A + A + A = 3 B + B + A = 5 C + C + B = 8 Then, A + B x C = ?
If a, b, c are three real numbers such that a + b + c = 7, a^2 + b^2 + c^2= 35 and a^3 + b^3 + C^3 = 151. Find the value of abc?