已知lgx=a,lgy=b,lgz=c,且a+b+c=0,求x1/b+1/c,y1/c+1/a,z1/a+1/b的值
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/06/30 20:15:43
已知lgx=a,lgy=b,lgz=c,且a+b+c=0,求x1/b+1/c,y1/c+1/a,z1/a+1/b的值
![](http://img.wesiedu.com/upload/2/ba/2ba8e43063f356a5c0bd86b5680c7c42.jpg)
![](http://img.wesiedu.com/upload/2/ba/2ba8e43063f356a5c0bd86b5680c7c42.jpg)
a+b+c=0
=>
lgx+lgy+lgz=0
=>lg(xyz)=0
=>xyz=1
x^(1/b+1/c)y^(1/a+1/c)z^(1/a+1/b)=
(xyz)^(1/a+1/b+1/c)/(x^1/a y^1/b z^1/c)
=1/(x^1/a y^1/b z^1/c)
lgx=a
=>1/algx=1=>lg(x^1/a)=1=>x^1/a=10
同理y^1/b=10 z^1/c=10
1/(x^1/a y^1/b z^1/c)=1/1000
x^(1/b+1/c)y^(1/a+1/c)z^(1/a+1/b)=1/1000
再问:![](http://img.wesiedu.com/upload/e/b1/eb18f12e5a2a662620d7052220be41a3.jpg)
再问:![](http://img.wesiedu.com/upload/a/19/a19132aac8faf97f909449b7fc9bdd49.jpg)
再问:![](http://img.wesiedu.com/upload/8/35/835f72f3ce010ab80c5dd518f4fcce3b.jpg)
=>
lgx+lgy+lgz=0
=>lg(xyz)=0
=>xyz=1
x^(1/b+1/c)y^(1/a+1/c)z^(1/a+1/b)=
(xyz)^(1/a+1/b+1/c)/(x^1/a y^1/b z^1/c)
=1/(x^1/a y^1/b z^1/c)
lgx=a
=>1/algx=1=>lg(x^1/a)=1=>x^1/a=10
同理y^1/b=10 z^1/c=10
1/(x^1/a y^1/b z^1/c)=1/1000
x^(1/b+1/c)y^(1/a+1/c)z^(1/a+1/b)=1/1000
再问:
![](http://img.wesiedu.com/upload/e/b1/eb18f12e5a2a662620d7052220be41a3.jpg)
再问:
![](http://img.wesiedu.com/upload/a/19/a19132aac8faf97f909449b7fc9bdd49.jpg)
再问:
![](http://img.wesiedu.com/upload/8/35/835f72f3ce010ab80c5dd518f4fcce3b.jpg)
已知lgx=a,lgy=b,lgz=c,且a+b+c=0,求x^(1/b+1/c) y^(1/a+1/c) z^(1/b
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