Consider the function, f(x)=2x3−9ax2+12a2x+1 has maximum value at p and minimum value at q so, f′(p)=0 and f′(q)=0 Now, f′(x)=6x2−18ax+12a2 Has roots p and q so, p+q=
18a
6
=3a And, pq=
12a2
6
=2a2 Solving above, p=a and q=2a since p2=q Given that, p2=q, thus a2=2a a2−2a=0 a(a−2)=0 a=2