Question

please solve this question
its urgent

Answer 1

use a^3 + b^3 +c^3 -3abc property

Answer 2

Given (2 - x)^3 + (2 - y)^3 + (2 - z)^3 - 3(2 - x)(2 - y)(2 - z).

It is in the form of a^3 + b^3 + c^3 - 3abc.

We know that a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).

Now,

Given that x + y + z = 6.

= > (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)

= > (2 - x + 2 - y + 2 - z)((2 - x)^2 + (2 - y)^2 + (2 - z)^2 - (2 - x)(2 - y) - (2 - y)(2 - z) - (2 - z)(2 - x))

= > (6 - (x + y + z))((2 - x)^2 + (2 - y)^2 + (2 - z)^2 - (2 - x)(2 - y) - (2 - y)(2 - z) - (2 - z)(2 - x))

= > (6 - 6)((2 - x)^2 + (2 - y)^2 + (2 - z)^2 + (2 - x)(2 - y) - (2 - y)(2 - z) - (2 - z)(2 - x)

= > (0)((2 - x)^2 + (2 - y)^2 + (2 - z)^2 + (2 - x)(2 - y) - (2 - y)(2 - z) - (2 - z)(2 - x)

= > 0.


Hope this helps!