题目内容
已知
=
=
，那么
=
．
| x |
| 6 |
| y |
| 4 |
| z |
| 3 |
| x2+3y2+2z2 |
| xy+yz+zx |
| 17 |
| 9 |
| 17 |
| 9 |
分析：先设
=
=
=k，那么x=6k，y=4k，z=3k，再把x、y、z都代入所求分式中，进行计算即可．
| x |
| 6 |
| y |
| 4 |
| z |
| 3 |
解答：解：设
=
=
=k，那么
x=6k，y=4k，z=3k，
∴
=
=
=
．
故答案是
．
| x |
| 6 |
| y |
| 4 |
| z |
| 3 |
x=6k，y=4k，z=3k，
∴
| x2+3y2+2z2 |
| xy+yz+zx |
| 36k2+3×16k2+2×9k2 |
| 6k×4k+4k×3k+3k×6k |
| 102k2 |
| 54k2 |
| 17 |
| 9 |
故答案是
| 17 |
| 9 |
点评：本题考查了分式的化简求值．解题的关键是把已知条件转化成整式形式．
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