已知实数x,y,m,n满足(x^2)+(y^2)=3,(m^2)+(n^2)=1,求mx+ny的最大值?
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 16:22:34
已知实数x,y,m,n满足(x^2)+(y^2)=3,(m^2)+(n^2)=1,求mx+ny的最大值?
已知实数x,y,m,n满足(x^2)+(y^2)=3,(m^2)+(n^2)=1,求mx+ny的最大值?
已知实数x,y,m,n满足(x^2)+(y^2)=3,(m^2)+(n^2)=1,求mx+ny的最大值?
一.设x=√3cosα,y=√3sinθ,m=cosθ,n=sinθ
则mx+ny=√3cosαcosθ+√3sinαsinθ=√3cos(α-θ)≤√3
二.(mx+ny)^2=m^2x^2+n^2y^2+2myxn≤m^2x^2+n^2y^2+m^2y^2+n^2x^2=
(x^2)+(y^2)=3,
(m^2)+(n^2)=1
两边分别相乘
m^2x^2+n^2y^2+m^2y^2+n^2x^2=3
所以(mx+ny)^2≤3
所以mx+ny≤√3
mx+ny≤1/2 (x^2+y^2+m^2+n^2)=1/2 *4=2
所以最大值为2
已知实数x,y,m,n满足(x^2)+(y^2)=3,(m^2)+(n^2)=1,求mx+ny的最大值?
已知向量m=(2,y),n=(x,1),且m垂直于n,则实数x,y满足关系式
已知实数m,n满足m^2 n^2=a,x,yx满足^2 y^2=b其中a,b为常数,求mx ny最小值已知实数m,n满足m^2+n^2=a,x,y满足x^2+y^2=b其中a,b为常数,求mx+ny最小值
已知实数X,Y满足2
已知实数xy满足x+2y
已知实数xy满足 x+y-2
已知实数x,y满足x^2+y^2=3(y>=0),若m=(y+1)/(x+3),n=2x+y,则m,n的取值范围是?
已知实数x,y满足x-y
已知实数X,Y满足{|x+y|
已知实数x,y,m,n满足x2+y2-4x-8y+19=0,m2+n2+8m+8n+28=0,则(x-m)2+(y-n)2的最大值是
已知单项式M、N满足2x(M+3x)=6x^2y^2+N,求M、N.
已知M={(x,y)|x^2+y^2=1},N={(x,y)|x/a+y/b=1,a、b属于正实数},若M交N非空,则a、b满足什么条件?要过程~
已知单项式M,N满足3x(M-5x)=6x^2y^3+N,求M,N
已知,单项式M,N满足2x(M+3x)=6x²y²+N,求M,N
已知实数m n满足:m/x-1+n/x+2=2x+7/(x-1)(x+2).求m和n
已知实数x.y满足(x+2)^2+y^2(
已知实数a b x y满足a^2+b^2= m,x^2+y^2=n.则ax+by的最大值是( )
已知实数M,N满足M^2+N^2=B,其中X^2+Y^2=B,其中A,B为常数,求MX+NY的最小值