已知实数X,Y,Z满足3的X次方=4的Y次方=6的Z次方大于1
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x+2y-z=6①x-y+2z=3②,①×2+②,得x+y=5,则y=5-x③,①+2×②,得x+z=4,则z=4-x④,把③④代入x2+y2+z2得,x2+(5-x)2+(4-x)2=3x2-18x
用x来表示y和z解方程组y-z=-x-y+2z=-3x两式相加得z=-4x把z=-4x代入y-z=-x中,得y=-5x所以x:y:z=x:(-5x):(-4x)=1:(-5):(-4)或x:y:z=-
三式相加:x+y+z+1/x+1/y+1/z=22/3三式相乘:xyz+y+x+1/z+z+1/x+1/y+1/xyz=28/3将1式代入2式得到xyz+22/3+1/xyz=28/3即:xyz+1/
用中学方法还是大学方法?再问:中学再答:柯西不等式:(x²+y²+z²)(2²+3²+1²)≥(2x+3y+z)=1因此x²+y&
|z-4|=|z+2i|即z到(4,0)和到(0,-2)距离相等所以(x-4)²+y²=x²+(y+2)²2x+4y=34^x+2^y=2^2x+2^y>=2√
x+2y-z=6,.(1)x-y+2z=3.(2)(1)-(2)y-z=1,y=1+z(1)+2(2)x+z=4,x=4-zx^2+y^2+z^2=(4-z)^2+(1+z)^2+z^2=3z^2-6
x-y=5x=5+yz^2=-xy-y-9=-(5+y)y-y-9=-y^2-6y-9=-(y+3)^2所以,z=0,y+3=0z=0,y=-3x=5+y=5-3=2x-2y+3z=2-2*(-3)+
x+2y-z=6所以2x+4y-2z=12因为x-y+2z=3两边相加3x+3y=15x+y=5带回去得到y=5-xz=4-x带回x^2+y^2+z^2=3x^2-18x+41=3(x^2-6x+9)
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)/2y,z可以看成m^2-[(17-3
x=5-yz2=(5-y)y+y-9=6y-y2-9=-(9-6y+y2)=-(y-3)2由题意,只有当该项为0时等式成立得y=3那么z=0x=2即原式=2+6+0=8
2x-3y-z=0..(1)x-2y+z=0...(2)(1)+(2):3x-5y=03x=5yy=3/5x将y=3/5x代入(1)z=2x-3y=2x-3*3/5x=x/5x:y:z=x:3/5x:
x+3y=6,2xy-z^2=6考虑到z^2=2xy-6>=0x+3y=6==>x=6-3y2(6-3y)y-6>=0==>y^2-2y+1y=1带回去,所以x=3,z=0
x+2y+3z=1的话,x=1/14;y=1/7;z=3/14三个数平方和最小值则为:1/14
3^x=4^y=6^zxlg3=ylg4=zlg63x
令(x+y)/2=(y+z)/3=(z+x)/7=kx+y=2ky+z=3kz+x=7kx=3ky=-kz=4k带入不等式26k^2+6ak+1>0凑完全平方式下面的应该会了吧懒得做了
|4x-4y+1|+1/3*√(2y+z)+(z^2-z+1/4)=0|4x-4y+1|+1/3*√(2y+z)+(z-1/2)^2=0则4x-4y+1=02y+z=0z-1/2=0解得z=1/2y=
由y+z=-xyz=1/x5构造一元二次方程m*m+x*m+1/x=0判别式=x*x-4/x〉0得x*x〉4/x显然x!=0若x〉0则x大于开3次根号4且此时yz同号都为负数命题结论成立若x小于0则y
移项,整理[(x-5)-4√(x-5)+4]+[(y-4)-4√(y-4)+4]+[(z-3)-4√(z-3)+4]=0[√(x-5)-2]²+[√(y-4)-2]²+[√(z-3
6x-2y-6z=0x-6y+6z=0解得x=24y/21,z=17y/21代入x+y+z/x-y+z=62/20=31/10-------------------------------------