内容正文:
书书书
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a=b=2
$%&'(
.
)%*
|x|+|x-2|≤a+b+'(,
%,-
|x|+|x-2|≤(a+b)min =4.
!
x<0
$
,
)%*.
-2x+2≤4,
/0
-1≤x<0;
!
0≤x≤2$,)%*.2≤4'(,
/0
0≤x≤2;
!
x>2
$
,
)%*.
2x-2≤4,/02<x≤3;
12
,
34
x
56789:
[-1,3].
(2)
;-
a>0,b>0,
<
4a+b=(4a+b) 1
a
+1( )b =5+
b
a
+4a
b
≥5+2
b
a
·
4a
槡 b =9,
!"#!
b
a
=4a
b
,
a+b=ab
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,
=
a=3
2
,b=3
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6>?@7
9.
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a,b,
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4a+b=8
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.
21.
!
:(1)
DEFGH<IJK
y≥4,
<
0≤x≤2,
2×3+x
3-x≥
{ 4L 2<x≤5,2(5-x)≥4{ ,
=
1≤x≤2L2<x≤3,M>1≤x≤3,
/0DEFGH$N?OPQRS
3
T
.
(2)
UVWXYZDEF5[\$N.
x
T
,
<]$V^XYZDEF5[\$N.
(x+3)
T
,
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0≤x≤2.
U
y1.V^XYZDEF5_`,y2.VWXY
ZDEF5_`
,y
.ab5DEF5_`
,
<
y1 =2[5-(x+3)]=4-2x,y2 =b·
3+x
3-x
,
;cd>
y=y1+y2 =4-2x+b·
3+x
3-x≥
4
B
[0,2]
2+'(
,
/0
b≥2x·
3-x
3+xB
[0,2]
2+'(
.
e
t=3+x,t∈[3,5],< b≥-2t+18( )t +18,
f
-2t+18( )t +18≤18-2·2 t·
18
槡 t =18-
槡122,!"#! t=
18
t
,
=
t= 槡32$%&'(,
" 槡32∈[3,5],JKcd.
/0
b≥18- 槡122,
g
b
5?@7.
18- 槡122.
22.
!
:(1)① ! m+1=0,= m=-1$,f(x)=
x-2,
hi)jcd
;
② ! m+1≠0,= m≠-1$,
;cP>
m+1>0,
Δ=m2-4(m+1)(m-1)≤0{ ,
M>
m>-1,
m≤- 槡
23
3 L
m≥ 槡
23
3
{ ,= m≥ 槡233.
/0
m [56789: 槡233,+ )∞ .
(2)
)%*
f(x)≥m,=(m+1)x2-mx-1≥0,
=
[(m+1)x+1](x-1)≥0,
①!m+1=0,=m=-1$,Mk.{x|x≥1};
② ! m+1>0,= m>-1$
(
,
x+ 1
m+ )1 (x-1)≥0,
l.
- 1
m+1
<0<1,
{/0Mk. x x≤ - 1m+1L x≥ }1 ;
③ ! m+1<0,= -2<m<-1$
(
,
x+ 1
m+ )1 (x-1)≤0,
l.
-2<m<-1,
/0
-1<m+1<0,
/0
- 1
m+1
>1,
{/0Mk. x 1≤x≤- 1m+ }1 .
(3)
l.)%*
f(x)≥05Mk.D," [-1,1]
D,
/0mnd5
x∈ [-1,1],)%*(m+1)x2 -
mx+m-1≥0+'(,
=
m(x2-x+1)≥-x2+1+'(,
l.
x2-x+1>0
+'(
,
/0
m≥
-x2+1
x2-x+1
=-1+ 2-x
x2-x+1
+'(
,
U
2-x=t,
<
t∈[1,3],x=2-t,
/ 0
2-x
x2-x+1
= t
(2-t)2-(2-t)+1
=
t
t2-3t+3
= 1
t+3
t
-3
≤
1
槡23-3
= 槡23+3
3
,
!"#!
t=槡3,= x=2-槡3$6%&,
]$ (, -x
2+1
x2-x+ )1 max = 槡
23
3
,
/0
m≥ 槡
23
3
.
g
m [56789: 槡233,+ )∞ .
"#$%&'()*
(
+
)
+,-$./0123#45
6
、
789
DDCABD CCDDBD
:;
:
1.cos105°-cos15°=cos(60°+45°)-cos(60°
-45°)=-2sin60°sin45°=-2×槡3
2
×槡2
2
=-槡6
2
.
2.
;cdPo
tan(α+45°)=
tanα+1
1-tanα
=2,
/0
tanα=
1
3
,
/0
cos2α=
cos2α-sin2α
cos2α+sin2α
=1-tan
2α
1+tan2α
=4
5
.
3.
!
x∈[0,1]$,π4≤ω
x+π
4≤
π
4
+ω,pC
f(x)
5qrBsN
[0,1]
2tG
1
uvwx:
2
5