If x + y + z = 6, then the value of (x – 1)^{3} + (y – 2)^{3} + (z – 3)^{3} is

Correct Answer is : 3 (x – 1)(y – 2)(z – 3)

SSC CPO SI and ASI 2012 Paper

Question : 128 of 200

Marks: +1, -0

If x + y + z = 6, then the value of (x – 1)

^{3}

+ (y – 2)

^{3}

+ (z – 3)

^{3}

Solution:

(4)Here, x+ y+ z+6= 0 , so
$ (x-1)+(y-2)+(z-3)=0.

I f

a+b+c=0 $ then

a^{3}+b^{3}+c^{3}=3 a b c

and hence,

(x-1)^{3}+(y-2)^{3}+(z-3)^{3}

=3(x-1)(y-2)(z-3)

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