Question

If 3x=a+b+c, then the value of (x-a)^3+(x-b)^3+(x-c)^3-3(x-a)(x-b)(x-c)is

Answer 1

we know that,a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)If a+b+c=0 then,a³+b³+c³-3abc=0×(a²+b²+c²-ab-bc-ca)=0 .....(1)
(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)let a=(x-a)b=(x-b)and c=(x-c)a+b+c=x-a+x-b+x-c=3x-(a+b+c)=3x-3x=0....(as a+b+c=3x)(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)=0

Answer 2

Answer:

we know that,a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)If a+b+c=0 then,a³+b³+c³-3abc=0×(a²+b²+c²-ab-bc-ca)=0 .....(1)

(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)let a=(x-a)b=(x-b)and c=(x-c)a+b+c=x-a+x-b+x-c=3x-(a+b+c)=3x-3x=0....(as a+b+c=3x)(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)=0