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第十章 数的开方·拔尖卷
2024
120
120
___________
___________
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1LN3 QN2025·RSTU·VWQX−
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3 8&0.2020020002&
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BL3 ]
CL2 ]
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2LN3 Q^_`a\ a Dbcde±m&fg a+1 Dbcdh m ijkNllQ
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BLNm2+1Q
CL± m+1
DL± m2+1
3LN3 QN23-24 mn o·pqrs·tuQ^v&X\wx&−10y 5zD{\K%8N Q
AL7 ]
BL6 ]
CL5 ]
DL4 ]
4LN3 QN22-23 |n x·}~·Q
1& 2& 3V]\vYc&(a,b)ij
JaJbD\&(8,2)y(10,10)ijD]\DeN Q
AL 6
BL 3
CL 2
DL1
5LN3 QN2025··KWQo\Y& x>3DeN Q
AL(−3)3
BL 2
CLπ
DL
3 27
6LN3 Q a Dbcdk 17.25&b Dcdk−8.69x Dbcdk±1.725&y Dcdk 86.9&
N Q
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ALx= 1
100a,y=−1000b
BLx= 1
100a,y=100b
CLx=100a,y= 1
100a
DLx= 1
1000a,y=−100b
7LN3 QN24-25 mn o·B·tYQ^v&X ¡¢£&OhKd¤¥
K]¦c
F§¨©ª&«¬®¯ °D±²³´µY&¶hK]=·=¸¹ºDFk24cm3&»¼;½¾¿¦c
F§¨DÀÁÂÃN Q
AL2cmÄ3cmz
BL3cmÄ4cmz
CL4cmÄ5cmz
DL5cmÄ6cmz
8LN3 QN24-25 mn o·¬Å·'ÆÇQ0Ã\ aÈb&Émax{a,b}DÊÉk
Ëa≥b&max{a,b}
=aËa<b&max{a,b}=bLÌ^
max{1,−2}=1LÍÎmax{ 29,a}= 29,max{ 29,b}=b&ÏaÄbk]ÐÑ
¦{\&ab−( 29)
2DcdkN Q
AL−1
BL1
CL−2
DL2
9LN3 QN23-24 mn o·ÒÓÔÕ·tYQdÖvYD×Ø&ËÙ®xk64&ÙºyDÚeNllQ
AL
3 2
BL 2
CL2
DL8
10LN3 QN24-25 |n x·}~BT·tYQÛo
a1= 1×2×3×4+1=5&a2= 2×3×4×5+1=11&
a3= 3×4×5×6+1=19&…&ÜE8KDÝ1&ÞJn]Dß_àkan&
1
a1+1+
1
a2+1+
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a3+1+⋅⋅⋅+
1
a2024+1
DÚeN Q
AL
1
2
BL
1
2025
CL
2023
4050
DL
506
1013
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11LN3 QN2025·}~âã·WäåÇQa2=42Ïb3=−27&(a+b)2=
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12LN3 QN2025·}~æç·áWQ\x&y&z
|x−3|+ y+1+(z+2)2=0&(x+y)2DÚk
L
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13LN3 QN24-25 mn o·}~7è·tYQÍÎ4a+1DK]bcde 5&−1−3bDcde 2&c e 7
D{\é&3a−2b+6cDbcde
L
14LN3 QN24-25 |n o·RSTêëT·tuQ\a&bX\wxDìí^vîj&ïð
|a+1|−(b−1)2
+ (a−b)2=
L
15LN3 QN24-25 mn o·Tñqò·tYQÍÎ
3 x−2+2−x=0&xDÚk
16LN3 QN24-25 mn o·óqôõ·tYQ^_ x eK]\&ö÷Þøù x Dú{\àk[x]&
Þ x DO\éàk{x}&û{x}=x−[x]L^
[4.2]=4,{4.2}=0.2,[−4.2]=−5,{−4.2}=0.8&ü
[ 15−2]=
3x+7
7
=4D{\
．．x DÚ8
]ÍÎ5x−3{x}=6&x=
L
JⅡ!
VL+,$N% 8 O$& 72 Q
17LN6 QN24-25 mn o·¬Å·tYQ¾
(1)2×(−3)+ 25−|−4|+
3 27
(2) 16+
3 −27
64×
−4
3
2
−|2−5|L
18LN6 QN24-25 mn o·ýqã·QiþZ[\O\éDcÿ^o
Ì^ 2&Āk 2D
{\ée 1&îāhĂ]\㥹{\é&ĆćeO\éLö÷;āh 2−1Ĉij 2DO\éL
(1) 7DO\ée_____
(2)ĉ 17DO\éex& 71D{\éey&üx+y−17DbcdL
19LN8 QN24-25 mn o·TñxĊ·QdÖoiċ,oČ$
x
15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
x2
225
228.01
231.04
234.09
237.16
240.25
243.36
246.49
249.64
252.81
(1) 243.36=______& 23716=______& 0.023104=______
(2) 25000yč]{\úĎďĐü 2.3DďđÚNß_ĒēĔ 0.01Q
(3)153< n<154& ĕĖD{\n8______]L
20LN8 QN24-25 mn o·ėĘ·tYQÉh(a,b)ijK]\0&ąYakęĚ\&b≥0Là
3 a=
m&−b=n&
\0(m,n)Ä(n,m)ěk\0(a,b)DK0“Ĝc0ě\0”LÌ^
\0(8,25)DĜc0ě\0k
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(2,−5)Ä(−5,2)L
ÎĝĞh
(1)ğĎĠº\0(27,1.69)DĜc0ě\0_______
(2)\0(x,y)DK]Ĝc0ě\0e −7, 3
2 &üx&yDÚ
(3)\0(a,b)DK]Ĝc0ě\0e(−4,−5)&üa+bDÚL
21LN10 QN24-25 mn o·ġĢĢ·tYQö÷Îģ&ęĚK]8[\yZ[\DÄkZ[\&ęĚ
K]kĤD8[\yK]Z[\DkZ[\&ĥĤyZ[\DkĤL»¼;¸
^_kx+b=0&ąY
kÈbk8[\&xkZ[\fgĦa8k=0&Ïb=0&Ö¼&+ħoČ$L
(1)^_(m−3) 2+2−n=0&ąYmÈnk8[\&m=___________&n=___________
(2)^_(n−2) 23+2m=8&ąYmÈnk8[\&ü3m−3
2nDbcdL
22LN10 Q^v①e» 8 ]ĨĩODcFĪæDīc&Fk 8L
(1)üºĂ]īcDÀÁ
(2)v①YĬĭéeK]¦c³ABCD&üºĬĭéD6ĮąįÁ
(3)Þ¦c³ABCDİĔ\wx&^v②&ı¸IJ A y−1ijĴ&fgIJ D X\wxijD\k_____L
23LN12 QN24-25 mn o·pq·tYQ# t ĵbcdÄcd&oiebcdÄcdDé
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bcd
cd
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KĶķ&^_K]\xDbcÃa&ûx2=a&f
gĂ]\xćĸ aDbcdNĹĸ áĺcdQ
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cde 0Ŀ\ŀ8bcdL
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Û(±1)4=1(±2)4=16
ŁłbcdÄcd&Ņ}ĺcdoÉ
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N2QŃņ1Ļ
①81 D}ĺcde_________②0 D}ĺcde_________③−625_________N)“8”
Ň“ŀ8”Q}ĺcdL
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①______________________________________________________
②______________________________________________________
③______________________________________________________
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4
−2
5
4
=_________
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3_________
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24LN12 QN24-25 mn o·BōèŎ·tYQŏŐo6DőŒ&+,Č$
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*O¦c³D¦c³&î¸ĔDO¦c³EFGHDįÁk________¦c³ABCDD6k________&
įÁk________L
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c³Ūū&ıÜDÁyŤzłk5:4LůŰù¾űŨeŲ;ųL
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