已知实数x y满足2x方 6xy 9y方-2x 1=0

将其看出关于x的方程5x²-(6y+4)x+2y²+2y+1=0其判别式△≥0而△=(6y+4)²-20(2y²+2y+1)=-4y²+8y-4=-4

实数x,y,z,满足那么x+y=6,z^2=xy-9,∴xy=z^+9,(x-y)^=(x+y)^-4xy=-4z^>=0,∴z=0,(x+y)^z=6^0=1.

∵|2x-3y+1|+(x+3y+5)的二次方=0∴2x-3y+1=0x+3y+5=0x=-2y=-1∴（-2x*y）的二次方（-y的二次方）×6xy平方的值=4x⁴y*(-y²

4x²+4xy+y²+2x+y-6=0(2x+y)²+(2x+y)-6=0(2x+y+3)(2x+y-2)=02x+y+3=0或2x+y-2=0y=-2x-3或y=2-2

k=(y+2)/(x+1)所以k就是过点(-1,-2)的直线的斜率x,y满足x^2+y^2=1所以就是求过点(-1,-2)的直线和单位圆有公共点是斜率的取值范围显然相切时有最值y+2=kx+kkx-y

x^2+y^2-6x+4y+13=0x^2-6x+9+y^2+4x+4=0(x-3)^2+(y+2)^2=0平方项恒非负,两平方项之和等于0,则两平方项都等于0.x-3=0x=3y+2=0y=-2x^

再问：图片看不全再答： 能看到了吧？

由已知x,y正实数由2x+2y+xy=5得5-xy=2(x+y)≧2*2√(xy)所以xy+4√(xy)-5≤0[√(xy)+5][√(xy)-1]≤00＜√(xy)≤1故,0

x^2+2xy+y^2-(x+y)-6=0(x+y)^2-(x+y)-6=0令x+y为a即a^2-a-6=0(a-3)(a+2)=0所以a=3或a=-2故x+y=3或-2

5x²-3xy+1/2y²-2x+1/2y+1/4=0两边乘以2得：10x²-6xy+y²-4x+y+1/2=0配方得：（3x-y-1/2)²+（x-

2x+y+6≥6+2√2xyxy≥6+2√2xy(√xy-√2)^2≥8√xy-√2≥2√2或√xy-√2≤-2√2（不可能）所以xy最小值是(3√2)^2=18-------------------

解由题知求xy的最大值,则x,y必定同号,不妨设x,y同正则由x^2+y^2+xy=1/3得1/3=xy+x²+y²即1/3-xy=x²+y²≥2xy即1/3≥

2x+y+6=xy化简得：Y=(2X+6)/(X-1)X不等于0因为正实数x.所以X>0所以X>1函数Y=(2X+6)/(X-1)是单调递增所以X=2为最小值,Y=10所以XY最小值为XY=20

分解因式有(x-3y)(2x-y)=0所以有x=3y或2x=y所以x:y=3:1或x:y=1:2

z=3x+y=13(x+2y)/6+5(x-4y)/6当x=5,y=2时取到,z最大值17

x²+y²-xy+2x-y+1=[3（x+1）²+(x-2y+1）²]/4=0,由于（x+1）²>=0且(x-2y+1）²>=0,则有x+1

10x²-2xy+y²+6x+1=0（3x+1）²＋(x-y)²=03x+1=0x-y=0所以x=y=-1/3x+y=-2/3再问：3x+1=x-y=再答：3x

x²+2xy-3y²=0(x+3y)(x-y)=0解得x=y或x=-3y又x,y为正数所以y=x；x=-3y舍(x²+xy+y²)/(x²-xy+y&

因为x,y,z都是实数,x+y=6,则y=6-x,代入z^2=xy-9得z^2=x（6-x）-9,整理的z^2=6x-x^2-9=-(x-3)^2,由z^2>=0,所以x=3,y=3,z=0,最后的答

2X方-4XY+4Y方-6X+9=0(x^2-4xy+4y^2)+(x^2-6x+9)=0(x-2y)^2+(x-3)^2=0所以有x-2y=0,x-3=0即有x=3,y=x/2=3/2x*根号8Y=