2000x^3=2001y^3=2002z^3
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/16 17:59:50
2000x^3=2001y^3=2002z^3
xyz>0
______________________ ______ _____ ____
3/ =3/ 3/ 3/
\/ 2000x^2+2001y^2+2002z^2 \/ 2000 + \/ 2001 \/ 2002
求 1/x+1/y+1/z 的值
Note:此为三次根号
______
3/
\/
xyz>0
______________________ ______ _____ ____
3/ =3/ 3/ 3/
\/ 2000x^2+2001y^2+2002z^2 \/ 2000 + \/ 2001 \/ 2002
求 1/x+1/y+1/z 的值
Note:此为三次根号
______
3/
\/
令2000x^3=2001y^3=2002z^3=N,题中方程立方得
2000x^2+2001y^2+2000z^2=(3次√2000+3次√2001+3次√2002)^3
两边同除以N
左边:(2000x^2+2001y^2+2000z^2)/N=2000x^2/N+2001y^2/N+2000z^2/N
=2000x^2/2000x^3+2001y^2/2001y^3+2000z^2/2002z^3
=1/x+1/y+1/z
右边:(3次√2000+3次√2001+3次√2002)^3/N
=[(3次√2000/3次√N)+(3次√2001/3次√N)+(3次√2002/3次√N)]^3
=[(3次√2000/3次√2000x^3)+(3次√2001/3次√2001y^3)+(3次√2002/3次√2002z^3)]
=(1/x+1/y+1/z)^3
即是 1/x+1/y+1/z=(1/x+1/y+1/z)^3
化简 (1/x+1/y+1/z)^2=1
因为 2000x^3=2001y^3=2002z^3且xyz大于0
所以 x>0,y>0,z>0
所以 1/x+1/y+1/z=1
2000x^2+2001y^2+2000z^2=(3次√2000+3次√2001+3次√2002)^3
两边同除以N
左边:(2000x^2+2001y^2+2000z^2)/N=2000x^2/N+2001y^2/N+2000z^2/N
=2000x^2/2000x^3+2001y^2/2001y^3+2000z^2/2002z^3
=1/x+1/y+1/z
右边:(3次√2000+3次√2001+3次√2002)^3/N
=[(3次√2000/3次√N)+(3次√2001/3次√N)+(3次√2002/3次√N)]^3
=[(3次√2000/3次√2000x^3)+(3次√2001/3次√2001y^3)+(3次√2002/3次√2002z^3)]
=(1/x+1/y+1/z)^3
即是 1/x+1/y+1/z=(1/x+1/y+1/z)^3
化简 (1/x+1/y+1/z)^2=1
因为 2000x^3=2001y^3=2002z^3且xyz大于0
所以 x>0,y>0,z>0
所以 1/x+1/y+1/z=1
试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y)
x/2=y/3=z/5 x+3y-z/x-3y+z
若{x+3y+10z=0 则 (x+y-z)/(x-y+z)
已知x,y,z 大于0,x+y+z=2,求证 xz/y(y+z)+zy/x(x+y)+yx/z(z+x)大于等于2/3
x=y/z=z/3,x+y+z =12,求2x+3y+4z是多少,
如果|x+y+z-6|+|2x+3y-z-12|+|2x-y-z|=0求x,y,
方程组{4x-3y-3z=0,x-3y+z=0,(x.y.z不等于0),求x/z和y/z的值?
4x-3y-3z=0 x-3y+z=0 并且X Y Z不等于0 求x:z 和y:z的值
3道高数题,1,函数F(x,y,z)=(e^x) * y * (z^2) ,其中z=z(x,y)是由x+y+z+xyz=
{x+y+z=1;x+3y+7z=-1;z+5y+8z=-2
x+2y=3 x+y+z=36 2x+y+z=15 2y=3z x-y=1 x+2y+z x-z=-1 2x+z-y=1
如果,根号x-3+| y-2 |+z^2=2z-1 求 (x+z)^y