Question

Find the value of (x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c),if a+b+c=3x

Answer 1

(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)

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

Answer 2

hope it helps !...............