m,n,p,q都是正的吧……
3=(m^2+n^2)(p^2+q^2)
=m^2*p^2+n^2*q^2+m^2*q^2+n^2*p^2
≥m^2*p^2+n^2*q^2+2mpnq
=(mp+nq)^2
∴mp+nq最大值为√3