若实数m,n,x,y满足m^2+n^2=a,x^2+y^2=b(a不等于b),mx+ny的最大值是

问题描述:

若实数m,n,x,y满足m^2+n^2=a,x^2+y^2=b(a不等于b),mx+ny的最大值是

是否学过三角函数呢?
设 m = √a sinA,n =√a cosA,x =√b sinB,y = √b cosB
mx + ny
= √(ab) * [ sinAsinB + cosAcosB]
= √(ab) * cos(A-B)
因此 最大值为 √ab