Question

prove that. (2x-3y)^3+(3y-4z)^3+(4z-2x)^3=3(2x-3y)(3y-4z)(4z-2x)​

Answer 1

Answer:

(2x−3y)

3

+(3y−4z)

3

+(4z−2x)

3

The equation can be written in this way

We know, (a)

3

+(b)

3

+(c)

3

−3abc=(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)

if a+b+c=0, then (a)

3

+(b)

3

+(c)

3

=3abc

Hence as we see, 2x−3y+3y−4z+4z−2x=0

(2x−3y)

3

+(3y−4z)

3

+(4z−2x)

3

=6(2x−3y)(3y−4z)(2z−x)