If the points(a3/(a−1),(a2−3)/(a−1)),(b3/(b−1) and (c3/(c−1),(c2−3)/(c−1)) where a, b, c are different from 1, lie on the line lx + my + n=0, then

Since the given points lie on the line lx + my + n= 0, a, b, c are the roots of the equation l(t3t−1)+m(t2−3t−1)+n=0or  lt3+mt2+nt−(3m+n)=0----1Hence, a+b+c=−ml ab+bc+ca=nl----2abc=3m+nlSo, from (1), (2), and (3), we getabc−(bc+ca+ab)+3(a+b+c)=0