Subject :IMO Class : Class 9
The value of (x – a)3 + (x – b)3 + (x – c)3 –3(x – a)(x – b)(x – c), when a + b + c = 3x is ______.
A 3
B 2
C 1
D 0
I couldn't understand the solution given by you
Ans 1:
Class : Class 9
the answer is 0 .
i hope you know the formula
a^3 + b^3 + c^3 - 3abc =0 , when a+b+c = 0.
take x-a = p, x-b=q and x-c=r.
so a/q we have to find p^3 + q^3 + r^3 - 3pqr.
now notice p+ q+ r= x-a+x-b+x-c = 3x-a-b-c = 0.
so p^3 + q^3 + r^3 - 3pqr =0 as p+q+r=0