Question

If the centroid of the triangle formed by the points (a,b),(b,c),(c,a) at the origin then a cube+ b cube + c cube =?

Answer 1

Answer:

3abc

Step-by-step explanation:

Centroid of a circle=(x1+x2+x3, y1+y2+y3)

Points are (a,b),(b,c) and (c,a)

= centroid (a+b+c, b+c+a) or (a+b+c, a+b+c)

Given: centroid lies at origin

(a+b+c,a+b+c)=(0,0)

=(a+b+c)=0    ......(i)

Now, using the identity,

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

Substituting the value of (a+b+c)=0 in the identity

=a³+b³+c³-3abc=0(a²+b²+c²-ab-bc-ca)

=a³+b³+c³-3abc=0

=a³+b³+c³=3abc

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