【答案】
分析:根據(jù)反比例函數(shù)圖象上點的坐標(biāo)特征,得出原式=
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,進而求出即可.
解答:解:T
1•T
2•…•T
n=x
1y
2•x
2y
3…x
ny
n+1=x
1•
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•x
2•
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•x
3•

…x
n•

=x
1•
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,
又因為x
1=1,n=9,
又因為T
1=1,所以x
1y
2=1,又因為x
1=1,所以y
2=1,即
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=1,又x
2=2,k=2,所以原式=
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,
于是T
1•T
2•…•T
9=x
1(y
2•x
2)(y
3•x
3)…(y
9•x
9)y
10=
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=
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=51.2.
故答案為:51.2.
點評:此題主要考查了反比例函數(shù)圖象上點的特征,解答此題的關(guān)鍵是將x
1•
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•x
2•

•x
3•

…x
n•
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的相同字母消掉,使原式化簡為一個僅含k的代數(shù)式,然后解答.