Question

If a + b + c = 3x then find the value of (x - a)3

+ (x - b)3

+ (x - c)3

- 3 (x - a ) ( x - b) ( x - c)​

Answer 1

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Answer 2

Answer:

(x−a)

3

+(x−b)

3

+(x−c)

3

−3(x−a)(x−b)(x−c) and a+b+c=3x

We know that a

3

+b

3

+c

3

−3abc=(a+b+c)(a

2

+b

2

+c

2

−ab−ac−bc)

If (a+b+c)=0, then.a

3

+b

3

+c

3

=3abc

Here,a=x−a

b=x−b

c=x−c and a+b+c=x−a+x−b+x−c=3x−(a+b+c)=3x−3x=0

Thus,(x−a)

3

+(x−b)

3

+(x−c)

3

−3(x−a)(x−b)(x−c)

=0