一道分式计算题!x^2+y^2+z^2 ----------------- =1 且x,y,z不等于0,求证1/x + 1/y +1/z=0 (x+y+z)^2 (分号不会打就凑合看看吧,还有我是初中生.)
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/06 06:34:42
![一道分式计算题!x^2+y^2+z^2 ----------------- =1 且x,y,z不等于0,求证1/x + 1/y +1/z=0 (x+y+z)^2 (分号不会打就凑合看看吧,还有我是初中生.)](/uploads/image/z/1849582-46-2.jpg?t=%E4%B8%80%E9%81%93%E5%88%86%E5%BC%8F%E8%AE%A1%E7%AE%97%E9%A2%98%21x%5E2%2By%5E2%2Bz%5E2+-----------------+%3D1+%E4%B8%94x%2Cy%2Cz%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C%E6%B1%82%E8%AF%811%2Fx+%2B+1%2Fy+%2B1%2Fz%3D0+%28x%2By%2Bz%29%5E2+%EF%BC%88%E5%88%86%E5%8F%B7%E4%B8%8D%E4%BC%9A%E6%89%93%E5%B0%B1%E5%87%91%E5%90%88%E7%9C%8B%E7%9C%8B%E5%90%A7%2C%E8%BF%98%E6%9C%89%E6%88%91%E6%98%AF%E5%88%9D%E4%B8%AD%E7%94%9F.%EF%BC%89)
一道分式计算题!x^2+y^2+z^2 ----------------- =1 且x,y,z不等于0,求证1/x + 1/y +1/z=0 (x+y+z)^2 (分号不会打就凑合看看吧,还有我是初中生.)
一道分式计算题!
x^2+y^2+z^2
----------------- =1 且x,y,z不等于0,求证1/x + 1/y +1/z=0
(x+y+z)^2
(分号不会打就凑合看看吧,还有我是初中生.)
一道分式计算题!x^2+y^2+z^2 ----------------- =1 且x,y,z不等于0,求证1/x + 1/y +1/z=0 (x+y+z)^2 (分号不会打就凑合看看吧,还有我是初中生.)
(x^2+y^2+z^2)/ x+y+z)^2=1
(x^2+y^2+z^2 )/(x^2+y^2+z^2+2xy+2xz+2yz)=1
x^2+y^2+z^2=x^2+y^2+z^2+2xy+2xz+2yz
2xy+2xz+2yz=0
xy+xz+yz=0
(xy+xz+yz)/xyz=0
1/x + 1/y +1/z=0
(x^2+y^2+z^2)/(x+y+z)^2 =1
x^2+y^2+z^2=x^2+y^2+z^2+2xy+2yz+2xz
xy+yz+xz=0
因为x,y,z不等于0,同除以xyz
1/z+1/x+1/y=0
x^2+y^2+z^2
----------------- =1
(x+y+z)^2
x^2+y^2+z^2 =(x+y+z)^2 =x^2+y^2+z^2+2xy+2xz+2yz
2xy+2xz+2yz=0,xy+xz+yz=0;且x,y,z不等于0,两边同时除以xyz,得1/x+1/y+1/z=0
得证:1/x + 1/y +1/z=0
x^2+y^2+z^2 =(x+y+z)^2
xy+yz+xz=0
两边同除以xyz,即得结果
x^2+y^2+z^2
----------------- =1 且x,y,z不等于0,
(x+y+z)^2
所以x^2+y^2+z^2 =(x+y+z)^2
2xy+2xz+2yz=0
xy+xz+yz=0
两边同除以xyz得
1/x+1/y+1/z=0
(x+y+z)^2 =x^2+y^2+z^2+2(xy+yz+xz)
=x^2+y^2+z^2
so:(xy+yz+xz)=0
1/x + 1/y +1/z=(xy+yz+xz)/xyz=0
注意我的回答和年清晰简单哦