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21 tháng 9
Bài 5:
a: \(B=2009\cdot2011\)
\(=\left(2010-1\right)\left(2010+1\right)\)
\(=2010\cdot2010-1=A-1\)
=>B<A
b: \(B=2019\cdot2021\)
\(=\left(2020-1\right)\left(2020+1\right)\)
\(=2020\cdot2020-1\)
=A-1
=>B<A
c: \(A=234234\cdot233=234\cdot233\cdot1001\)
\(B=233233\cdot234=233\cdot234\cdot1001\)
Do đó: A=B
d: \(A=123\cdot137137=123\cdot137\cdot1001\)
\(B=137\cdot123123=137\cdot123\cdot1001\)
Do đó: A=B
Bài 4:
a: \(391-125<\overline{26x}<184+84\)
=>\(266<\overline{26x}<268\)
=>\(\overline{26x}=267\)
=>x=7
b: \(935+167<\overline{110x}<1240-135\)
=>\(1102<\overline{110x}<1105\)
=>x∈{3;4}
c: \(135\cdot12<\overline{162x}<4869:3\)
=>\(1620<\overline{162x}<1623\)
=>x∈{1;2}
d: \(11268:3<\overline{375x}<235\cdot16\)
=>\(3756<\overline{375x}<3760\)
=>x∈{7;8;9}
Bài 3:
l: x+125=492
=>x=492-125=367
m: 327-x=129
=>x=327-129=198
n: 124+(118-x)=217
=>118-x=217-124=93
=>x=118-93=25
o: 89-(73-x)=20
=>73-x=89-20=69
=>x=73-69=4
p: 198-(x+4)=120
=>x+4=198-120=78
=>x=78-4=74
q: (x+7)-25=23
=>x+7=25+23=48
=>x=48-7=41
r: 140:(x-8)=7
=>x-8=140:7=20
=>x=20+8=28
s: 4(x+41)=400
=>x+41=400:4=100
=>x=100-41=59
t: 4(3x-4)-2=18
=>4(3x-4)=2+18=20
=>3x-4=5
=>3x=9
=>x=3
u: 123-5(x+4)=38
=>5(x+4)=123-38=85
=>x+4=85:5=17
=>x=17-4=13
v: 231-(x-6)=1339:13
=>231-(x-6)=103
=>x-6=231-103=128
=>x=128+6=134
w: (x-36):18+12=14
=>(x-36):18=2
=>\(x-36=2\cdot18=36\)
=>x=36+36=72
21 tháng 9
Bài 5:
a: \(B=2009\cdot2011\)
\(=\left(2010-1\right)\left(2010+1\right)\)
\(=2010\cdot2010-1=A-1\)
=>B<A
b: \(B=2019\cdot2021\)
\(=\left(2020-1\right)\left(2020+1\right)\)
\(=2020\cdot2020-1\)
=A-1
=>B<A
c: \(A=234234\cdot233=234\cdot233\cdot1001\)
\(B=233233\cdot234=233\cdot234\cdot1001\)
Do đó: A=B
d: \(A=123\cdot137137=123\cdot137\cdot1001\)
\(B=137\cdot123123=137\cdot123\cdot1001\)
Do đó: A=B
Bài 4:
a: \(391-125<\overline{26x}<184+84\)
=>\(266<\overline{26x}<268\)
=>\(\overline{26x}=267\)
=>x=7
b: \(935+167<\overline{110x}<1240-135\)
=>\(1102<\overline{110x}<1105\)
=>x∈{3;4}
c: \(135\cdot12<\overline{162x}<4869:3\)
=>\(1620<\overline{162x}<1623\)
=>x∈{1;2}
d: \(11268:3<\overline{375x}<235\cdot16\)
=>\(3756<\overline{375x}<3760\)
=>x∈{7;8;9}
Bài 3:
l: x+125=492
=>x=492-125=367
m: 327-x=129
=>x=327-129=198
n: 124+(118-x)=217
=>118-x=217-124=93
=>x=118-93=25
o: 89-(73-x)=20
=>73-x=89-20=69
=>x=73-69=4
p: 198-(x+4)=120
=>x+4=198-120=78
=>x=78-4=74
q: (x+7)-25=23
=>x+7=25+23=48
=>x=48-7=41
r: 140:(x-8)=7
=>x-8=140:7=20
=>x=20+8=28
s: 4(x+41)=400
=>x+41=400:4=100
=>x=100-41=59
t: 4(3x-4)-2=18
=>4(3x-4)=2+18=20
=>3x-4=5
=>3x=9
=>x=3
u: 123-5(x+4)=38
=>5(x+4)=123-38=85
=>x+4=85:5=17
=>x=17-4=13
v: 231-(x-6)=1339:13
=>231-(x-6)=103
=>x-6=231-103=128
=>x=128+6=134
w: (x-36):18+12=14
=>(x-36):18=2
=>\(x-36=2\cdot18=36\)
=>x=36+36=72
21 tháng 9
Bài 5:
a: \(B=2009\cdot2011\)
\(=\left(2010-1\right)\left(2010+1\right)\)
\(=2010\cdot2010-1=A-1\)
=>B<A
b: \(B=2019\cdot2021\)
\(=\left(2020-1\right)\left(2020+1\right)\)
\(=2020\cdot2020-1\)
=A-1
=>B<A
c: \(A=234234\cdot233=234\cdot233\cdot1001\)
\(B=233233\cdot234=233\cdot234\cdot1001\)
Do đó: A=B
d: \(A=123\cdot137137=123\cdot137\cdot1001\)
\(B=137\cdot123123=137\cdot123\cdot1001\)
Do đó: A=B
Bài 4:
a: \(391-125<\overline{26x}<184+84\)
=>\(266<\overline{26x}<268\)
=>\(\overline{26x}=267\)
=>x=7
b: \(935+167<\overline{110x}<1240-135\)
=>\(1102<\overline{110x}<1105\)
=>x∈{3;4}
c: \(135\cdot12<\overline{162x}<4869:3\)
=>\(1620<\overline{162x}<1623\)
=>x∈{1;2}
d: \(11268:3<\overline{375x}<235\cdot16\)
=>\(3756<\overline{375x}<3760\)
=>x∈{7;8;9}
Bài 3:
l: x+125=492
=>x=492-125=367
m: 327-x=129
=>x=327-129=198
n: 124+(118-x)=217
=>118-x=217-124=93
=>x=118-93=25
o: 89-(73-x)=20
=>73-x=89-20=69
=>x=73-69=4
p: 198-(x+4)=120
=>x+4=198-120=78
=>x=78-4=74
q: (x+7)-25=23
=>x+7=25+23=48
=>x=48-7=41
r: 140:(x-8)=7
=>x-8=140:7=20
=>x=20+8=28
s: 4(x+41)=400
=>x+41=400:4=100
=>x=100-41=59
t: 4(3x-4)-2=18
=>4(3x-4)=2+18=20
=>3x-4=5
=>3x=9
=>x=3
u: 123-5(x+4)=38
=>5(x+4)=123-38=85
=>x+4=85:5=17
=>x=17-4=13
v: 231-(x-6)=1339:13
=>231-(x-6)=103
=>x-6=231-103=128
=>x=128+6=134
w: (x-36):18+12=14
=>(x-36):18=2
=>\(x-36=2\cdot18=36\)
=>x=36+36=72
22 tháng 9
d: \(48\cdot26+24\cdot148\)
\(=48\cdot26+48\cdot74\)
\(=48\cdot\left(26+74\right)=48\cdot100=4800\)
e: \(23\cdot48+92\cdot88\)
\(=23\cdot4\cdot12+92\cdot88\)
\(=92\cdot12+92\cdot88=92\cdot100=9200\)
b: \(89\cdot25+89\cdot74+89\)
\(=89\cdot\left(25+74+1\right)\)
\(=89\cdot100=8900\)
12 giờ trước (13:23)
Bài 7: Ta có: \(a\cdot b=ƯCLN\left(a;b\right)\cdot BCN\mathbb{N}\left(a;b\right)\)
=>\(a\cdot b=10\cdot900=9000\)
ƯCLN(a;b)=10
=>a⋮10; b⋮10
ab=9000
mà a⋮10 và b⋮10 và a<b
nên (a;b)∈{(10;900);(20;450);(30;300);(50;180);(60;150);(90;100)}
mà ƯCLN(a;b)=10
nên (a;b)∈{(10;900);(20;450);(50;180);(90;100)}
Bài 5:
ƯCLN(a;b)=6
=>a⋮6; b⋮6
ab=216
mà a⋮6; b⋮6
nên (a;b)∈{(6;36);(12;18);(18;12);(36;6)}
Bài 4: Gọi hai số tự nhiên cần tìm là a,b
ƯCLN(a;b)=5
=>a⋮5; b⋮5
Ta có: ab=300
mà a⋮5; b⋮5
nên (a;b)∈{(5;60);(60;5);(10;30);(30;10);(15;20);(20;15)}
Bài 1:
a: ƯCLN(a;b)=6
=>a⋮6 và b⋮6
a+b=96
mà a⋮6 và b⋮6
nên (a;b)∈{(6;90);(90;6);(12;84);(84;12);(18;78);(78;18);(24;72);(72;24);(30;66);(66;30);(36;60);(60;36);(42;54);(54;42);(48;48)}
mà ƯCLN(a;b)=6
nên (a;b)∈{(6;90);(90;6);(18;78);(78;18);(30;66);(66;30);(42;54);(54;42)}
b: ƯCLN(a;b)=4
=>a⋮4 và b⋮4
a+b=16
mà a⋮4; b⋮4 và a>b
nên (a;b)∈{(12;4);(8;8)}
mà ƯCLN(a;b)=4
nên (a;b)=(12;4)
NV
Nguyễn Việt Lâm
Giáo viên
5 tháng 9
20.
a.
\(4^{n}=256\)
\(4^{n}=4^4\)
\(n=4\)
b.
\(9^{5n-8}=81\)
\(9^{5n-8}=9^2\)
5n-8=2
5n=10
n=2
c.
\(3^{n+2}:27=3\)
\(3^{n+2}=27.3\)
\(3^{n+2}=81\)
\(3^{n+2}=3^4\)
n+2=4
n=2
d.
\(8^{n+2}.2^3=8^5\)
\(8^{n+2}=8^5:2^3\)
\(8^{n+2}=8^4\)
n+2=4
n=2
NV
Nguyễn Việt Lâm
Giáo viên
5 tháng 9
21.
a.
\(30-2x^2=12\)
\(2x^2=30-12\)
\(2x^2=18\)
\(x^2=18:2=9\)
\(x^2=3^2\)
\(x=\pm3\)
b.
\(\left(9-2x\right)^3=125\)
\(\left(9-2x\right)^3=5^3\)
\(9-2x=5\)
2x=9-5=4
x=2
c.
\(\left(2x-2\right)^4=0\)
2x-2=0
2x=2
x=1
d.
\(\left(x+5\right)^3=\left(2x\right)^3\)
x+5=2x
2x-x=5
x=5
6 tháng 9
20.
4^n=256
4^n=4^4
n=4
9^5n-8=81
9^5n-8=9^2
5n-8=2
5n=10
n=2
3^n+2:27=3
3^n+2:3^3=3
3^n+2-3=3
n+2-3=1
n=2
8^n+2.2^3=8^5
8^n+2.8=8^5
8^n+2+1=8^5
n+2+1=5
n=2
21.
30-2x^2=12
2x^2=30-12
2x^2=18
x^2=9
x^2=3^2
x=3
(9-2x)^3=125
(9-2x)^3=5^3
(9-2x)=5
2x=4
x=2
(2x-2)^4=0
(2x-2)=0
2x=2
x=1
(x+5)^3=(2x)^3
x+5=2x
x+5-2x=0
(x-2x)=-5
-x=-5
x=5
6 tháng 9
20:
a: \(4^{n}=256\)
=>\(4^{n}=4^4\)
=>n=4
b: \(9^{5n-8}=81\)
=>\(9^{5n-8}=9^2\)
=>5n-8=2
=>5n=10
=>n=2
c: \(3^{n+2}:27=3\)
=>\(3^{n+2}=27\cdot3=81=3^4\)
=>n+2=4
=>n=2
d: \(8^{n+2}\cdot2^3=8^5\)
=>\(8^{n+2}=8^5:8=8^4\)
=>n+2=4
=>n=2
Bài 21:
a: \(30-2x^2=12\)
=>\(2x^2=30-12=18\)
=>\(x^2=9\)
mà x>=0(do x là số tự nhiên)
nên x=3
b: \(\left(9-2x\right)^3=125\)
=>9-2x=5
=>2x=4
=>x=2
c: \(\left(2x-2\right)^4=0\)
=>2x-2=0
=>2x=2
=>x=1
d: \(\left(x+5\right)^3=\left(2x\right)^3\)
=>2x=x+5
=>2x-x=5
=>x=5
Bài 1:
a: 2x+3=15
=>2x=15-3=12
=>\(x=\frac{12}{2}=6\)
b: 28-3x=13
=>\(3x=28-13=15\)
=>\(x=\frac{15}{3}=5\)
c: \(\left(x-1954\right)\cdot5=50\)
=>x-1954=50:5=10
=>x=10+1954=1964
d: 30(60-x)=30
=>60-x=1
=>x=60-1=59
Bài 2:
a: x+99:3=55
=>x+33=55
=>x=55-33=22
b: (x-25):15=20
=>\(x-25=20\cdot15=300\)
=>x=300+25=325
c: \(7\left(3x-15\right)=42\)
=>\(3x-15=\frac{42}{7}=6\)
=>3x=15+6=21
=>\(x=\frac{21}{3}=7\)
d: \(x\left(x+1\right)=2+4+6+\cdots+2500\)
=>\(x\left(x+1\right)=2\left(1+2+3+\cdots+1250\right)\)
=>\(x\left(x+1\right)=2\cdot1250\cdot\frac{1251}{2}=1250\cdot1251\)
=>\(x^2+x-1250\cdot1251=0\)
=>(x+1251)(x-1250)=0
=>\(\left[\begin{array}{l}x+1251=0\\ x-1250=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-1251\\ x=1250\end{array}\right.\)
Bài 1:
a: \(46\cdot99=46\cdot\left(100-1\right)=46\cdot100-46\)
=4600-46
=4554
b: \(47\cdot98=47\cdot\left(100-2\right)=47\cdot100-47\cdot2\)
=4700-94
=4604
c: \(18\cdot19=18\left(20-1\right)=18\cdot20-18\)
=360-18
=342
d: \(24\cdot198=24\left(200-2\right)\)
\(=24\cdot200-24\cdot2\)
=4800-48
=4752
Bài 2:
a: \(1800\cdot5=18\cdot100\cdot5=90\cdot100=9000\)
b: \(36\cdot25=25\cdot4\cdot9=100\cdot9=900\)
c: 36600:50=3660:5=732
d: 220000:5000=220:5=44
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