设实数M,N,P,Q.满足MQ-NP=1,M^2+N^2+P^2+Q^2-MN+PQ=1.求MNPQ

问题描述:

设实数M,N,P,Q.满足MQ-NP=1,M^2+N^2+P^2+Q^2-MN+PQ=1.求MNPQ

第一步由:m²+n²+p²+q²-mn+pq=1.将式子进行配方,可得(m-n)²+(p+q)²+mn-pq=1.【式1】第二步,再次将原式填项配方:m²+n²+p²+q²-mn+pq+2mq-2mq+2np-2np=1.化为...