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a) Đề:........
= 18. (73 + 15 + 12)
= 18. 100
= 18000
b) Đề nên sửa 23 thành 25
= 100 : { 250 : [ 450 - (4. 125 - 4.25)]}
= 100 : { 250 : [ 450 - (500 - 100)]}
= 100 : { 250 : [ 450 - 400 ]}
= 100 : { 250 : 50 }
= 100 : 5
= 20
a) 18.73+15.18+12.18
=18.(73+15+12)
=18.100
=1800
b) (37+63):{250:[450-(4.53-22.23)]}
=(37+63):{250:[450-(22.53-22.23)]}
=100:{250:[450-22.(53-23)]}
=100:{250:[450-22.102]}
=100:{250:[450-408]}
=100:{250:42}
=100:\(\frac{125}{21}\)
=\(\frac{84}{5}\)
\(2.11^{25}:11^{23}-3^5:\left(1^{2018}+2^3\right)-60\)
\(=2.\left(11^{25}:11^{23}\right)-3^5:\left(1+8\right)-60\)
\(=2.11^2-3^5:9-60\)
\(=2.121-3^5:3^2-60\)
\(=242-3^3-60\)
\(=242-27-60\)
\(=215-60\)
\(=155\)
Đặt \(A=2^0+2^1+..+2^{100}\)
\(\Rightarrow2A=2^1+2^2+..+2^{101}\)
lấy hiệu hai phương trình ta có
\(A=2^{101}-2^0=2^{101}-1\)
.\(B=5^1+5^2+..+5^{200}\)
\(\Rightarrow5B=5^2+5^3+..+5^{201}\)
Lấy hiệu hai phương trình ta có :
\(4B=5^{201}-5\Rightarrow B=\frac{5^{201}-5}{4}\)
số sh cua tong A bang so hang cua day so cach deu 1 don vi tu 1 den 60
so sh cua tong A la:(60-1):1+1=60 (sh)
Cu 3 sh lien tiep cua tong A nhom thanh 1 nhom thi ta duoc so nhom la : 60: 3=20(nhom)
khi do : A = (2+2^2+2^3)+(2^4+2^5+2^6)+(2^7+2^8+2^9)+....+(2^58+2^59+2^60)
A=(2+2.2+2.2^2)+(2^4+2^4.2+2^4.2^2)+(2^7+2^7.2+2^7.2^2)+.....+(2^58
2^58.2+2^58.2^2)
A=2(1+2+2^2)+2^4(1+2+2^2)+2^7(1+2+2^2)+...+2^58(1+2+2^2)
A=2.7+2^4.7+2^7.7+...+2^58.7
A=7(2+2^4+2^7+...+2^58)
Vi 7 chia het cho 7
2+2^4+2^7+...+2^58 thuoc N
Suy ra 7(2+2^4+2^7+...+2^58) chia het cho 7
hay A chia het cho 7
Vay A chia het cho 7
Câu 1:
abc >/ 100 ; bca >/ 100 ; cab>/100
< = > abc + bca + cab >/300
< = > abc + bca + cab >/ 111
Bài 1:
a) 23=2.2.2=823=2.2.2=8;
24=23.2=8.2=1624=23.2=8.2=16;
25=24.2=16.2=3225=24.2=16.2=32;
26=25.2=32.2=6426=25.2=32.2=64;
27=26.2=64.2=12827=26.2=64.2=128;
28=27.2=128.2=25628=27.2=128.2=256;
29=28.2=256.2=51229=28.2=256.2=512;
210=29.2=512.2=1024210=29.2=512.2=1024
b) 32=3.3=932=3.3=9;
33=32.3=9.3=2733=32.3=9.3=27;
34=33.3=27.3=8134=33.3=27.3=81;
35=34.3=81.3=24335=34.3=81.3=243.
c) 42=4.4=1642=4.4=16;
43=42.4=16.4=6443=42.4=16.4=64;
44=43.4=64.4=25644=43.4=64.4=256.
d) 52=5.5=2552=5.5=25;
53=52.5=25.5=12553=52.5=25.5=125;
54=53.5=125.5=62554=53.5=125.5=625.
e) 62=6.6=3662=6.6=36;
63=62.6=36.6=21663=62.6=36.6=216;
64=63.6=216.6=129664=63.6=216.6=1296.
a)2^3.17-14+2^3.3^2
=8.17-14+8.9
=136-14+72
=194
b)102-272+|-15|-23
=-170+15-23
=-178
c)95:93 -32.3
=92-3
=78
a) 23 . 17 - 14 + 23 . 32
= 23 . ( 17 + 32 ) - 14
= 8 . ( 17 + 9 ) - 14
= 8 . 26 - 14
= 208 - 14
= 194
b) 102 - 272 + |-15| + (-23)
= 102 - 272 + 15 - 23
= - 170 + 15 - 23
= - 155 - 23
= - 178
c) 95 : 93 - 32 . 3
= 92 - 33
= 81 - 27
= 54
Bài 1:
a,(2x-15):13+51=64
=> (2x-15):13=64-51
=> (2x-15):13=13
=>(2x-15)=1
=> 2x =16
=> x = 8
Vậy: x= 8
a) \(4.5^2-81:3^2=4.25-81:9=100-9=91\)
b) \(3^3.23-3^3.19=3^3.\left(23-19\right)=27.4=108\)
c) \(2^4.5-[131-\left(13-4\right)^2]=16.5-\left(131-9^2\right)=80-\left(131-81\right)=80-50=30\)
d) \(100:\left\{250:\left[450-\left(4.5^3-2^2.25\right)\right]\right\}\)
\(=100:\left\{250:\left[450-4.\left(125-25\right)\right]\right\}\)
\(=100:\left[250:\left(450-4.100\right)\right]\)
\(=100:\left[250:\left(450-400\right)\right]=100:\left(250:50\right)=100:5=20\)