Question

buddies solve this easy question if u know

$\large{QUESTION}$

If the centroid of the triangle formed by the points (a,b) , (b,c) , (c,a) is at the origin then ,
${a}^{3} + {b}^{3} + {c}^{3} =$
(a) abc
(b) a+b+c
(c) 3abc
(d) 0


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Answer 1

Answer:

It's Option C. 3abc.............

Step-by-step explanation:

a+b+c/3 , a+b+c/3 = (0,0)

=> a+b+c/3 = 0

=> a+b+c = 0

As according to the Identity

a³ + b³ + c³ - 3abc = 0 [ substitute a+b+c in place of 0]

a³+b³+c³ = 3abc

Hope it helps you........

Answer 2

Answer:

according to question,

centroid of triangle is in origin which means that coordinates of centroid of triangle will be equal to (0,0).

formula to find centroid of triangle in co-ordinate geometry »

[x,y]=[(x1+x2+x3)/3,(y1+y2+y3)/3]

Here, (x,y)=(0,0),(x1,y1)=(a,b),

(x2,y2)=(b,c),(x3,y3)=(c,a)

putting the values,

» [0,0]=[(a+b+c)/3,(b+c+a)/3]

comparing the values,

» 0=(a+b+c)/3

» 0=a+b+c

A/Q ,

3a+3b+3c=3(a+b+c)=3×0=0

ANSWER is 0………….