若实数mnpq满足条件m+n+p+q=22 mp=nq=100
问题描述：
若实数mnpq满足条件m+n+p+q=22 mp=nq=100
则(m+n)(n+p)(p+q)(q+m)整体开根号的值为
答
m+n+p+q=22 平方得[(m+n)+(p+q)]^2=22^2(m+n)^2+(p+q)^2+2(m+n)(p+q)=484m^2+n^2+p^2+q^2+2(mn+pq+np+mq)+400=484m^2+n^2+p^2+q^2+2(mn+pq+np+mq)=84(m+n)(n+p)(p+q)(q+m)=[(m+n)(p+q)][(n+p)(q+m)]=(200+mq+np)(200...