实数a,b,x,y满足ax+by=3,ax的平方+by的平方=7,ax的3次方+by的3次方=16,ax的4次方+by的4次方=42,那ax的5次方+by的5次方=?

[(ax)+(by)]^2-[(ax)^2+(by)^2]=2axby=9-7=2
axby=1
(ax+by)[(ax)^4+(by)^4]=(ax)^5+(by)^5+ax(by)^4+by(ax)^4=(ax)^5+(by)^5+axby[(ax)^3+(by)^3]
=(ax)^5+(by)^5+(ax)^3+(by)^3
(ax)^5+(by)^5=(ax+by)[(ax)^4+(by)^4]-[(ax)^3+(by)^3]=42*3-16=110