已知实数x、y、z满足3x+2y+2z=17,则x^2+y^2+z^2的最小值是( )
来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/17 12:41:56
已知实数x、y、z满足3x+2y+2z=17,则x^2+y^2+z^2的最小值是()已知实数x、y、z满足3x+2y+2z=17,则x^2+y^2+z^2的最小值是()已知实数x、y、z满足3x+2y
已知实数x、y、z满足3x+2y+2z=17,则x^2+y^2+z^2的最小值是( )
已知实数x、y、z满足3x+2y+2z=17,则x^2+y^2+z^2的最小值是( )
已知实数x、y、z满足3x+2y+2z=17,则x^2+y^2+z^2的最小值是( )
设x^2+y^2+z^2=t
由3x+2y+2z=17得:y+z=(17-3x)/2
又y^2+z^2=t-x^2可变得:yz=(17-3x)^2/8+(x^2-t)/2
y,z可以看成m^2-[(17-3x)/2]+(17-3x)^2/8+(x^2-t)/2=0的两根
于是由判别式>=0列式得:(17-3x)^2/4-4[(17-3x)^2/8+(x^2-t)/2]>=0
化简得:t>={17(x-3)^2+136}/8
当x=3时,t取得最小值t=136/8=17即是x^2+y^2+z^2的最小值是(17)
使用线性规划,特别简单
x=3,y=2,z=2(运算结果)
Object. min Z=x^2+y^2+z^2=17
s.t. 3x+2y+2z=17
已知实数x y z满足x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3,求x+y+z的值
已知实数x y z满足x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3,求x+y+z的值
已知实数x,y,z满足x+y+z=2根号x-1+2根号y-1+2根号z-1求X+2Y+3Z
已知实数xyz满足x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3求x+y+z的值
已知实数x,y,z满足关系式2x-3y-z=0,x-2y+z=0,求x比y比z的值
已知实数 x y z 满足x+y-z=0 ,3x-y+2z=0 则x :y :z
已知实数x,y,z,满足那么x+y=6,z^2=xy-9,求(x+y)^z
已知实数x,y,z满足x+y+z=1,x^2+y^2+z^2=1/2求X,Y,Z∈{0,2/3},已知实数x,y,z满足x+y+z=1,x^2+y^2+z^2=1/2求证X,Y,Z∈{0,2/3},
已知实数x,y,z满足x+y=5,z^2=xy+y-9,那么x+2y+3z=?我很着急
已知实数x.y.z满足x+y=5及z的2次方=xy+y-9则x+2y+3z=?
已知实数x,y,z满足x+y=5,z^2=xy+y-9,那么x+2y+3z=?
已知实数x,y,z满足x-y=5,z^2=-xy-y-9,求x-2y+3z的值
已知实数x,y,z,满足x+y=5,z²=xy+y=9,求x+2y+3Z的值
已知实数x、y、z满足x+y=5,z的平方=xy+y-9,那么x+2y+3z=( )
已知x,y,z均为实数,且满足:x+2y-z=6,x-y+2z=3.求x+y+z的最小值
已知三个实数x,y,z满足条件(z-x)^2-4(x-y)(y-z)=0,求证:x,y,z成等差数列
已知非负实数x,y,z满足x+y+z=3 (2),求证x^2/(1+x^4)+y^2/(1+y^4)+z^2/(1+z^4)≤1/(1+x)+1/(1+y)+1/(1+z)
已知实数x,y,z满足:x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3,则x+y+z=