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Question
If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 + b3 + c3 =
Options
abc
0
a + b + c
3 abc
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Solution
The co-ordinates of the vertices are (a, b); (b, c) and (c, a)
The co-ordinate of the centroid is (0, 0)
We know that the co-ordinates of the centroid of a triangle whose vertices are `(x_1 ,y_1) ,(x_2 , y_2) ,(x_3 ,y_3)` is
`((x_1 + x_2 + x_3 )/3 , ( y_1 + y_2 + y_3)/ 3)`
So,
`(0,0) = ((a + b + c) /3 , (b + c+a ) /3)`
Compare individual terms on both the sides-
`(a + b + c) / 3 = 0`
Therefore,
`a + b+ c = 0`
We have to find the value of -
`a^3 + b^3 +c^3`
Now as we know that if,
a + b +c = 0
Then,
`a^3 + b^3 +c^3 = 3abc`
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