If a,b,c are all different and the equations ax+a2y+a3+1z=0, bx+b2y+b3+1z=0 ,  cx+c2y+c3+1z=0 have a nonzero solution, then

Given equation have non zero solution ⇒aa2a3+1bb2b3+1cc2c3+1=0⇒aa2abb2b3cc2c3+aa21bb21cc21=0⇒abc1aa21bb21cc2+1aa21bb21cc2=0⇒(abc+1)1aa21bb21cc2=0⇒abc=−1