Question

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

Answer 1

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