Question

Centroid of a triangle formed by the points (a,b), (b,c) and (c,a) is at origin. If a^3 + b^3 + c^3 - 3abc = k^2, then find the value of k.​

Answer 1

Answer:

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Answer 2

LET G(0,0) BE THE CENTROID OF ΔABC

VERTICES : A(a,b), B(b,c), C(c,a)

    centroid of triangle = [$\frac{x1+x2+x3}{3} \frac{y1+y2+y3}{3}$]

                            (0,0) = {$\frac{a+b+c}{3} \frac{b+c+a}{3}$}

                                 0 = $\frac{a+b+c}{3}$

                        ∴ a+b+c = 0

     ⇔ if a+b+c = 0 then a³+b³+c³-3abc = 0

                         ⇒ k² = 0

                         ⇒ k = 0