题目内容
已知:
=
=
,设A=
,B=
,C=
,求A、B、C的值,并且比较它们大小.
| x |
| 2 |
| y |
| 7 |
| z |
| 5 |
| x |
| x+y+z |
| x+z |
| y |
| x+y-z |
| x |
分析:令
=
=
=k,则x=2k,y=7k,z=5k,分别代入A、B、C即可求得其值.
| x |
| 2 |
| y |
| 7 |
| z |
| 5 |
解答:解:令
=
=
=k,
则x=2k,y=7k,z=5k,
故A=
=
=
=
,
B=
=
=1,
C=
=
=2,
故C>B>A.
| x |
| 2 |
| y |
| 7 |
| z |
| 5 |
则x=2k,y=7k,z=5k,
故A=
| x |
| x+y+z |
| 2k |
| 2k+7k+5k |
| 2k |
| 14k |
| 1 |
| 7 |
B=
| x+z |
| y |
| 2k+5k |
| 7k |
C=
| x+y-z |
| x |
| 2k+7k-5k |
| 2k |
故C>B>A.
点评:本题考查了比例的性质,解题的关键是设出一个系数,用这个系数表示出x、y、z的值后代入即可求解.
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