If three equations are consistent (a+1)^3 x+(a+2)^3 y=(a+3)^3(a+1) x+(a+2) y=a+3x+y=1 , then a is equal to

Step-by-step solution

Since the equations are consistent D =0 | array ccc (a+1)^3 & (a+2)^3 & -(a+3)^3 (a+1) & (a+2) & -(a+3) 1 & 1 & -1 array |=0 aligned & Put u=(a+1), v=a+2, w=a+3 & u-v=-1, v-w z-1, w-u=2 & u+v+w=3 a+6 aligned | array ccc u^3 & v^3 & w^3 u & v & w 1 & 1 & 1 array |=0 aligned & (u-v)(v-w)(w-u)(u+v+w)=0 & (-1)(-1)(2)(3 a+6)=0 & i.e. a=-2 aligned