Question

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

Answer 1

we know that
a^3 + b^3 + c^3 =3abc
or, a+b+c = 0

so, x - a + x -b +x - c = 0
or, 3x - ( a + b + c) = 0
or, 3x - 0 = 0
or, x = 0

we put the value of x in it
we get , (-a)^3 +(-b)^3 +(-c) ^3 +3abc

we know that 3abc = a^3 + b^3 + c^3

so, - a^3 - b^3 -c^3 + a^3 + b^3 + c^3
= 0