यदि `x+y+z=6` है तो `(x-1)^(3)+(y-2)^(3)+(z-3)^(3)` का मान ज्ञात करें।

Options

A. `(3x-1)(y+2)(z-3)`
B. `3(x+1)(y-2)(z-3)`
C. `3(x-1)(y-2)(z+3)`
D. `3(x-1)(y-2)(z-3)`

Answer

D

Explanation

`x+y+z=6`
`(x-1)^(3)+(y-2)^(3)+(z-3)^(3)`
`:.` as `x=y+z=6`
Take values
`(1+2+3)=6`
`:. (1-1)^(3)+(2-2)^(3)+(3-3)^(2)=0`
Now assume values in options.
optiond d satisfies the given relation.
Hence d is correct.