The value of a for which system of equation , `a^3x+(a+1)^3y+(a+2)^3z=0, ax+(a+1)y+(a+2)z=0, x+y+z=0,` has a non-zero solution is:

Options

A. 1
B. 0
C. `-1`
D. None of these

Answer

C

Explanation

For non-zero solution,
`|{:(a^(3), (a+1)^(3), (a+2)^(3)),(a, (a+1),(a+2)),(1,1,1):}|=0`
`implies-|{:(1,1,1),(a,(a+1),(a+2)),(a^(3),(a+1)^(3),(a+2)^(3)):}|=0`
`-(a-a-1)(a+1-a-2)(a+2-a)xx(a+a+1+a+2)=0`
`implies-2(3a+3)=0`
`impliesa=-1`
`[because|{:(1,1,1),(x,y,z),(x^(3),y^(3), z^(3)):}|=(x-y)(y-z)(z-x)(x+y+z)]`