x2+2xy+4y2=6,求z=x2+4y2的最小值
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x2-xy=-3①,2xy-y2=-8②,①×2+②×3得:2x2-2xy+6xy-3y2=-6-24=-30,则2x2+4xy-3y2=-30.
X2+Y2+8X+6Y+25=0x²+8x+16+y²+6y+9=0(x+4)²+(y+3)²=0∴x+4=0y+3=0x=-4y=-3X2+4XY+4Y2分之
X2+Y2+8X+6Y+25=0x^2+y^2+8x+6y+25=0x^2+8x+16+y^2+6y+9=0(X+4)^2+(y+3)^2=0x=-4y=-3(x^2-4y^2)/(x^2+4xy+4
设2/x=3/y=4/z=1/k则x=2k,y=3k,z=4k将xyz代入x2+y2+z2/xy+yz+zx原式=(4k^2+9k^2+16k^2)/(6k^2+12k^2+8k^2)=29k^2/2
你问错了吧?不是X2-4Y+Y2+6Y+根号(Z-3)+13=0,而是X2-4X+Y2+6Y+根号(Z-3)+13=0吧?那样的话就可以解了:原式就可合并为:(X-2)2+(Y-3)2+根号(Z-3)
5x2—3xy—4y2—11xy—7x2+2y2=-2x2-2y2-14xy=-2(x2+y2)-14xy=-14+28=14
x+y=7xy=27^2=(x+y)^2=x^2+2xy+y^2=x^2+y^2+2*2x^2+y^2=45(1)y=7-xx(7-x)=2x^2-7x+2=0x=(7+41^(1/2))/2或x=(
x^2-4x+y^2+6y+√z-3+13=0配方得到:x^2-4x+4-4+y^2+6y+9-9+√z-3+13=0(x-2)^2+(y+3)^2+√z-3=0解得:x=2,y=-3.把x,y代入方
1.x^2+y^2+z^2=(x+y+z)^2-2*(xy+yz+xz)=82.配方(x-1)^2+(y+2)^2+(z-3)^2=0x=1y=-2z=3x+y+z=2再问:兄弟我敬佩你,如果你能帮我
再问:你确定吗?再答:我保证再答:亲,那一步不明白可以问再问:你省略了一步吧!再答:能看明白吗再问:no再答: 再答:是不是这部再问:那么第一步是怎么得来的呢?再答:第一步不是你
10拆成1+9X2-2X+1+Y2-6Y+9=0(X-1)2+(Y-3)2=0平方大于等于0,相加等于0,若有一个大于0,则另一个小于0,不成立.所以两个都等于0所以X-1=0,Y-3=0X=1,Y=
令x/3=y/4=z/6=K则x=3K,y=4K,c=6K(xy+yz+xz)/(X2+y2+z2)=(3K*4K+4K*6K+3K*6K)/(3K*3K+4K*4K+6K*6K)=54K2/61K2
∵x2+y2=7,xy=-2,∴7x2-3xy-2y2-11xy-5x2+4y2,=(7x2-5x2)+(4y2-2y2)-(3xy+11xy),=2x2+2y2-14xy,=2(x2+y2)-14x
6x2-xy-15y2=(2x+3y)(3x-5y)=0,所以x=-3/2y或x=5/3y
∵x2+y2+z2≤2x+4y-6z-14,∴x2+y2+z2-2x-4y+6z+14≤0,∴x2-2x+1+y2-4y+4+z2+6z+9≤0,∴(x-1)2+(y-2)2+(z+3)2≤0,∴x-
换元.可设x=a+b,y=a-b.则z=2(a²+b²)-(a²-b²)-2(a+b)+(a-b)=a²-a+3b²-3b=[a-(1/2)
∵4x2+8xy+9y2=4x2+2xy+9y2+6xy=2(2x2+xy)+3(3y2+2xy),2x2+xy=6,3y2+2xy=9,∴2(2x2+xy)+3(3y2+2xy)=2×6+3×9=3
3x2+2y2-6x=0x2+y2=1/2(6x-x2)=9/2-1/2(x2-6x+9)=9/2-2-1/2(x-3)2当x=3时,Z最大=4.5
因为x²+4y²+x²y²-6xy+1=0(x²-4xy+4y²)+(x²y²-2xy+1)=0(x-2y)²