1)
a)2008.213+2008.87
=2008(213+87)
=2008.300
=602400
b)2007.75+25.2007
=2007(75+25)
=2007.100
=200700
c)28.76+28.13+11.28
=28(76+13+11)
=28.100
=2800
d)6^2:43+2.5^2
=36:43+2.25
=36/43+50
=36/43+2150/43
=2186/43
e)3^3.118-3^3.18
=27.118-27.18
=27(118-18)
=27.100
=2700
f)4.5^2-3.2^3
=4.25-3.8
=100-24
=76
g)15.2^3+4.3-5.7
=15.8+12-35
=120+12-35
=97
h)2^2.3-(1^10+8):3^2
=4.3-(1+8):9
=12-9:9
=12-1
=11
i)4^8:4^5-(1^30+17):3^2
=4^3-(1+17):9
=64-18:9
=64-2
=62
j)150-[10^2-(14-11)^2.2007^0]
=150-[100-3^2.1]
=150-[100-9]
=150-91
=59
k)12:{390:[500-(125+35.7)]}
=12:{390:[500-(125+245)]}
=12:{390:[500-370]}
=12:{390:130}
=12:3
=4
l)1+2+..+2013
SSH=(2013-1):1+1
=2012:1+1
=2013
Tổng=(2013+1).2013:2
=2014.2013:2
=2027091
m)21.7^2-11.7^2+90.7^2+49.125.16
=21.49-11.49+90.49+49.2000
=49(21-11+90+2000)
=49.2100
=102900
n)(2^2+2^1+2^2+2^3).2^0.2^1.2^2.2^3
=(4+2+4+8).1.2.4.8
=18.1.2.4.8
=36.4.8
=144.8
=1152
Bài 2:
a)B={x∈NI30<x≤40}
⇒B={31; 32; 33; 34; 35; 36; 37; 38; 39; 40}
b)4(3x-4)-2=18
12x-16-2=18
12x-18=18
12x=18+18
12x=0
x=0:12
⇒x∈{∅}
c)(105-x):2^5=3^0+1
(105-x):32=1+1
(105-x):32=2
(105-x)=2.32
(105-x)=64
x=105-64
x=41
d)2x-138=2^2.3^2
2x-138=4.9
2x-138=36
2x=36+138
2x=174
x=174:2
x=87
e)(6x-39)28=5628
(6x-39)=5628:28
(6x-39)=201
6x=201+39
6x=240
x=240:6
x=40
f)(9x+2)3=60
27x+6=60
27x=60-6
27x=54
x=54:27
x=2
g)(26-3x):5+71=75
(26-3x):5=75-71
(26-3x):5=4
(26-3x)=4.5
(26-3x)=20
3x=26-20
3x=3
x=3:3
x=1
h)5^x+1=125
5^x+1=5^3
x+1=3
x=3-1
x=2
Bài 3:
a)126÷x; 210÷x và 10<x<40
⇒x∈ƯC(126; 210)
Ta có:
126=2x3^2x7
210=2x3x5x7
⇒ƯCLN(210; 126)=2x3x7=42
⇒ƯC(126; 210)=Ư(42)={1; 2; 3; 6; 7; 14; 21; 42}
Mà 10<x<40, nên:
⇒x∈{14; 21}
b)x÷18; x÷15; x÷12 và 200≤x≤500
⇒x∈BC(18; 15; 12)
Ta có:
18=2x3^2
15=3x5
12=2^2x3
⇒BCNN(18; 15; 12)=2^2x3^2x5=180
⇒BC(18; 12; 15)=B(180)={0; 180; 360; ...}
Mà 200≤x≤500 nên:
⇒x∈{360}
c)x:2; x:3; x:4; x:5 thì đều dư 1 và 100<x<150
⇒(x-1)∈BC(2; 3; 4; 5)
Ta có:
2=2.1
3=1.3
4=2^2
5=5.1
⇒BCNN(2; 3; 4; 5)=2x3x4x5=120
⇒BC(2; 3; 4; 5)=B(120)={0; 120; 240; 360;...}
⇒x∈{1; 121; 241; 361;...}
Mà 100<x<150, nên:
x∈{121; 241; 361; 481}
