内容正文:
!13"# 67 )*3089
1.'(><?�7¡ÝZ£¤<!"#& (A )
A.(2狓-狔)(狓+2狔)
B.(-2狓+狔)(-2狓-狔)
C.(-狓-2狔)(狓-2狔)
D.(2狓+狔)(-2狓+狔)
2.2犪+犫=3,2犪-犫=1,04犪2-犫2= 3 .
3.!":
(1)(2犪-3犫)(-2犪-3犫);
!
:
"#=(-3犫)2-(2犪)2
=9犫2-4犪2;
(2)(狓3+2狔
2)(狓3-2狔
2);
!
:
"#=(狓3)2-(2狔
2)2
=狓6-4狔
4;
(3)(-2狋-1)2;
!
:
"#=4狋2+4狋+1;
(4)(
1
5
狓+
1
10
狔)
2.
!
:
"#=
1
25
狓2+
1
25
狓狔+
1
100
狔
2.
4.V�1,ªpß.犪#)Z;tu?xy67
pß.犫#p)Z;,¦×ØËÙ犃犅xl,
5x3#h�tu¸3V�2#P¹º;.
(1)��1?���ü+".犛1,�2?��
�ü+".犛2,��5¡m犪,犫#�9<¥
¦犛1J犛2;
(2)�2`�Ìx[I7¿~#de<.
!
:(1)∵0�j�2Ez/犪,��j�2Ez/犫,∴
犛1=犪
2-犫2.犛2=
1
2
(2犪+2犫)(犪-犫)=(犪+犫)(犪-
犫);
(2)±²%&':(犪+犫)(犪-犫)=犪2-犫2.
5.9£Ú�,��C2,1¡�;#+"yY
Û6b�9ÜP<
,
V�1,1YÛKÇÝ
Z¤<
:(犪+犫)2=犪2+2犪犫+犫2.
(1)V�2(�?>pßZ;^pÞOP),�
¡h��t#Z¤=�2?���ü#+"
(
�|}
);
Z¤1: 4犪犫 .
Z¤2: (犪+犫)
2-(犪-犫)2 .
(2)ä(1)?h��t#Z¤,S7×�¼�
#P<
?
�MNº7P<36
;
(3)BC(2犿+狀)2=13,(2犿-狀)2=5,�µ
¡
(2)?#P<,=犿狀#D.
!
:(2)(犪+犫)2-(犪-犫)2=4犪犫,¹º.
¤¥
:∵(犪+犫)2-(犪-犫)2
=犪2+2犪犫+犫2-(犪2-2犪犫+犫2)
=4犪b.
∴(犪+犫)2-(犪-犫)2=4犪b;
(3)$(2)':(2犿+狀)2-(2犿-狀)2=8犿狀.
∵(2犿+狀)2=13,(2犿-狀)2=5,
∴8犿狀=13-5,犿狀=1.
6.}Ý!":
(1)20232-2024×2022;
!
:
"#=20232-(2023+1)(2023-1)
=20232-(20232-1)
=1;
(2)2982.
!
:
"#=2982-22+4=(298+2)(298-2)+4
=300×296+4=88800+4
=88804;
!»¼
:
"#=(300-2)2=3002-2×300×2+22
=88804
.
·52·
7.!":2(3+1)(32+1)(34+1)(38+1)(316+
1)(332+1)+1.
!
:
"#=(3-1)(3+1)(32+1)(34+1)(38+1)
(316+1)(332+1)+1
=(32-1)(32+1)(34+1)(38+1)(316+1)(332+1)+1
=(34-1)(34+1)(38+1)(316+1)(332+1)+1
=(332-1)(332+1)+1
=3
64.
8.BC狓2-狔
2=-18,/狓-狔=3,0狓+狔=
-6 .
9.(1)!":50.42-49.62= 80 ;
(2)!":20202-2020×4038+20192= 1 .
10.!":(1-
1
22
)(1-
1
32
)……(1-
1
992
)(1-
1
1002
).
!
:
"#=(1-
1
2
)(1+
1
2
)(1-
1
3
)(1+
1
3
)×…
×(1-
1
99
)(1+
1
99
)(1-
1
100
)(1+
1
100
)
=
1
2
×
3
2
×
2
3
×
4
3
×
3
4
×……×
100
99
×
99
100
×
101
100
=
1
2
×
101
100
=
101
200
.
11.!":
(1)(狓+狔)(狓
2+狔
2)(狓-狔)(狓
4+狔
4);
(2)(犪-2犫+3犮)(犪+2犫-3犮).
!
:(1)"#=(狓-狔)(狓+狔)(狓
2+狔
2)(狓4+狔
4)
=(狓2-狔
2)(狓2+狔
2)(狓4+狔
4)
=(狓4-狔
4)(狓4+狔
4)
=狓8-狔
8;
(2)