作业帮5x+6y+7z=1,则x^2+y^2+z^2+(x+y+z)^2的最小值为
来源：学生作业帮助网 编辑：作业帮 时间：2024/09/05 18:23:31
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5x+6y+7z=1,则x^2+y^2+z^2+(x+y+z)^2的最小值为
5x+6y+7z=1,则x^2+y^2+z^2+(x+y+z)^2的最小值为
5x+6y+7z=1,则x^2+y^2+z^2+(x+y+z)^2的最小值为
w=x^2+y^2+z^2+(x+y+z)^2+t(5x+6y+7z-1)
&w/&x=2x+2(x+y+z)+5t=0 (1)
&w/&y=2y+2(x+y+z)+6t=0 (2)
&w/&z=2z+2(x+y+z)+7t=0 (3)
5x+6y+7z=1 (4)
联立(1)(2)(3)(4) 解得 x=1/58 y=3/58 z=5/58 t=-2/29
得到唯一的可能极值点
最小值wmin=(1/58)^2+(3/58)^2+(5/58)^2+(1/58+3/58+5/58)^2=1/29
^2是不是√2
已知x+2y-3z=0,5x-6y+7z=1;则x:y:z=?把“5z-6y+7z=1”改成“5x-6y+7z=0”
1.{x:y:z=3:4:5 2x+3y-5z=-142.{x-y-z=-1 3x+5y+7z=11 4x-y+2z=-13.{x+y=1 x+z=0 2x+y+2z=44.{x-y+z=-3 2x-y-z=-2 -3x+y+z=-15.{x-y+z=-3 3x+y-4z=6 2x+y-z=36.{x-2y+5z=16 2x+y-5z=7 2x-y+z=38
..1.x+y+z=26,2.4y+3z=7,y-z=1,3x+2z=17,x+2y-z=18 9x-7y=173.x-7y+3z=17 4.2x+4y+3z=95x-6y-z=24 3x-2y+5z=113x+7y-2z=1 5x-6y+7z=131.x+y+z=26,y-z=1x+2y-z=18 2.4y+3z=7,3x+2z=11,9x-7y=17 3.x-7y+3z=17 5x-6y-z=24 3x+7y-2z=14.2x+4y+3z=93x-2y+5z=11 5x-6y+7z=13
(1)2X+4Y+3Z=93X-2Y+5Z=115X-6Y+7Z=13(2)X:Y=3:2Y:Z=5:4X+Y+Z=66(3)3X-Y+Z=32X+Y-3Z=11X+Y+Z=13以上3个题目为三元一次方程~
若X:Y:Z=5:6:7那么(Y-X):(Y+Z)和(X+2Y+3Z):(3X+2Y+Z)
4X+3Y-2Z=-7,5X-6Y+Z=1,2X+Z=-2
4X+3Y-2Z=-7,5X-6Y+Z=1,2X+Z=-2
方程组3x+y-4z=1 2x-y-2z=6 5x+3y-3z= --1/2{负二分之一} x=?y=?z=?3x+2y+z=13 x+y+2z=7 2x+3y-z=12 x=?y=?z=?
5x+6y+7z=1,则x^2+y^2+z^2+(x+y+z)^2的最小值为
{x+y+z=1;x+3y+7z=-1;z+5y+8z=-2
x+Y+Z=1 X+3Y+7Z=-1 X+5Y+8Z=2x+Y+Z=1X+3Y+7Z=-1X+5Y+8Z=2
(1)X+Y=15,Y+Z=-6,Z+X=7.(2)X+Y=-14,Y+Z=-7,Z+X=9.(3)X+Y=0,Y+Z=-1,Z+X=-1.
x-y+z=-1 5x+2y-z=6 4x-3y+2z=-5
2x+5y+4z=6,3x+y-7z=-4,x+y-z=?
若4x=7y+5z,2x+y=z,则x:y:z的值为
已知2x+5y+4z=6 3x+y-7z=-4求x+y-z
5x+3y+2z=2011 4x+6y+7z=2012 求x+y+z
{x+y+z=1 {x+3y+7z=-1 {x+5y+8z=2