由韦达定理知：p+q=-a,pq=a .
则(p-2q)(q-2p)=pq-2p²-2q²+4pq
=9pq-2(p²+2pq+q²)
=9pq-2(p+q)²
=9a-2a²
=81/8-[(√2)a-9/(2√2)]²≤81/8 .
即：(p-2q)(q-2p)的最大值是81/8 .