Find the following system of equations is consistent,
`(a+1)^3x+(a+2)^3y=(a+3)^3`, `(a+1)x+(a+2)y=a+3, x+y=1`, then find the value of `a`

Answer

`a=-2`

Explanation

Since the equations are consistent we have
`Delta=0`
`rArr |{:((a+1)^(3),,(a+2)^(3),,-(a+3)^(3)),((a+1),,(a+2),,-(a+3)),(1,,1,,-1):}|=0`
`" or " |{:((a+1)^(3),,(a+2)^(3),,(a+3)^(3)),((a+1),,(a+2),,(a+3)),(1,,1,,1):}|=0`
`" or " [(a+1)-(a+2)][(a+2)-(a+3)][(a+3)-(a+1)]`
`xx[a+1+a+2+a+3]=0`
`" or " a=-2`