内容正文:
!犪>
1
犪
,-1<犪<0;犪>1,3"S�lA?6
1
犪
<
狓<犪.
}kU©
:
①!犪<-1;0<犪<1",S�lA?6犪<狓<
1
犪
;
②!犪=±1",S�l<?.
③!犪>1;-1<犪<0",S�lA?6
1
犪
<狓<犪.
(5)①!犪<0",S�lA?6
2
犪
<狓<2.
②!犪=0",S�lA?6狓<2.
③!0<犪<1",S�lA?6狓<2;狓>
2
犪
.
④!犪=1",S�lA?6狓≠2.
⑤!犪>1",S�lA?6狓<
2
犪
;狓>2.
(6)④!犪<0",S�lA?6狓<
-1- 1+4槡 犪
2犪
;
狓>
-1- 1-4槡 犪
2犪
.
②!犪=0",S�lA?6狓<-1.
③!0<犪<
1
4
"
,
S�lA?6
-1- 1-4槡 犪
2犪
<狓
<
-1+ 1-4槡 犪
2犪
.
④!犪≥
1
4
"
,
S�l<?.
9.94狓2-5狓-6=(4狓+3)(狓-2)<0,@-
3
4
<狓<2.
rl= (狓-3)槡 2+|狓+1|=|狓-3|+|狓+1|
=-(狓-3)+(狓+1)=4.
10.76wxªyK1>0,U]Δ=(-狆)2-4×9≤0,
U]-6≤狆≤6.
11.«�
狔=犽狓+2犽+1,
狔=-狓+4{ . U]
狓=
-(2犽-3)
犽+1
,
狔=
6犽+1
犽+1
烅
烄
烆
.
¬e®¯§°
,
#
-(2犽-3)
犽+1
>0,
6犽+1
犽+1
<0
烅
烄
烆
.
f
-1<犽<
3
2
,
-1<犽<-
1
6
烅
烄
烆
.
U]-1<犽<-
1
6
.
12. 9 ± ² X : 犪<0,� > ³ � � � � @
-
犫
犪
=α+β.
犮
犪
=αβ
烅
烄
烆
.
#S�l犮狓2+犫狓+犪>0X�6
犪αβ狓
2-犪(α+β)狓+犪>0,fαβ狓
2-(α+β)狓+1<0.
U]
(α狓-1)(β狓-1)<0.
760<α<β,U]
1
α
>
1
β
,
U] 狓-
1( )α 狓-
1( )
β
<
0.U]犮狓2+犫狓+犪<0A?6
1
β
<狓<
1
α
.
&7' O@P
1.6 -
1
4
2.4 3.25
4.763-2狓-狓2≥0,U]´¨µ狓ABCDE6-3
≤狓≤1.p狔= -(狓+1)2+槡 4,!狓=-1",狔max=
2;!狓=-3;狓=1",狔min=0.
5.76狔= 槡狓-
2
槡( )狓
2
+ 槡2 2-2(狓>0),U]狔min
= 槡2 2-2.
6.76犪2+犫2-(犪犫+犪+犫-1)=
1
2
[(犪-犫)2+(犪-1)2
+(犫-1)2]=0,U]犪=犫=1,U]犪+犫=2.
7.76犪2+犫2+犮2-(犪犫+犫犮+犮犪)=
1
2
(2犪2+2犫2+2犮2
-2犪犫-2犫犮-2犮犪)=
1
2
[(犪-犫)2+(犫-犮)2+(犮-犪)2]
≥0,U]犪2+犫2+犮2≥犪犫+犫犮+犮犪.
8.76狓+2狔=1,U]狕=3狔2+2(1-2狔)=3狔2-4狔+
2=3狔-( )23
2
+
2
3
.�狔≥0,狓=1-2狔≥0,U]0≤
狔≤
1
2
.U]!狔=0",狕max=2;!狔=
1
2
"
,狕min
=
3
4
.
9.9¶:@(狓-2槡狓+1)+[(狔-1)-2 狔-槡 1+1]+
[(狕-2)-2 狕-槡 2+1]=0.U](槡狓-1)2+
( 狔-槡 1-1)2+( 狕-槡 2-1)2=0.U]狓=1,狔=2,狕
=3.
10.rlX¨·6 犪-
犫( )2
2
+3
犫
2
-( )1
2
+(犮-1)2
≤0.
�76 犪-
犫( )2
2
+3
犫
2
-( )1
2
+(犮-1)2≥0,U]
犪-
犫( )2
2
+3
犫
2
-( )1
2
+(犮-1)2=0.U]犪=1,犫
=2,犮=1.
11.76狓2+3狓+1=0,U]狓+3+
1
狓
=0,狓+
1
狓
=-
3,狓2+
1
狓2
= 狓+
1( )狓
2
-2=7
.
·56·
2 3 4 5
U]狓3+
1
狓3
= 狓+
1( )狓 狓2+
1
狓2
-( )1 =-18,狓4+
1
狓4
= 狓2+
1
狓( )2
2
-2=47.
U]狓7+
1
狓7
= 狓3+
1
狓( )3 狓4+
1
狓( )4 - 狓+
1( )狓 =
-18×47+3=-843.
12.76犪>犫,U]犫-犪<0,U]-犪3