题目内容
观察下列各式及其验证过程:2
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;,3
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•
验证:2
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=
=
=
=
=
;3
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=
=
=
=
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•
(1)按照上面结论猜想4
的结果,并写出验证过程;
(2)根据对上述各式规律,写出用n(n为正整数,且n≥2)表示的等式并给出证明.
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2+
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3+
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验证:2
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2+
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2+
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3+
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3+
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(1)按照上面结论猜想4
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(2)根据对上述各式规律,写出用n(n为正整数,且n≥2)表示的等式并给出证明.
分析:(1)根据已知中二次根式的化简即可得出答案.
(2)利用(1)中计算结果,即可得出二次根式的变化规律,进而得出答案即可.
(2)利用(1)中计算结果,即可得出二次根式的变化规律,进而得出答案即可.
解答:解:(1)4
=
.
4
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,
=
,
=
,
=
,
=
=
;
(2)n
,
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•
,
=
,
=
,
=n
.
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4+
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4
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=
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=
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=
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=
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=
4+
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4+
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(2)n
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=
n+
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n+
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=
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=
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=n
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点评:此题主要考查了数字变化规律,根据已知得出根式内外变化规律是解题关键.
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