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x+1 + x+2 + x+3 + x +4 + x+5 = 45
x + x + x + x + x = 45 -1 -2 -3 -4 -5
5x = 30
x =6
![](https://rs.olm.vn/images/avt/0.png?1311)
(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=45
( x + x + x + x + x ) + ( 1 + 2 + 3 + 4 + 5 ) = 45
5x + 15 = 45
5x = 45 - 15
5x = 30
x = 30 : 5
x = 6
![](https://rs.olm.vn/images/avt/0.png?1311)
(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=45
<=> (x+x+x+x+x)+(1+2+3+4+5)=45
<=> 5x+15=45
<=> 5x=30
<=> x=6
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(x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) = 45
x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 45
(x + x + x + x + x) + (1 + 2 + 3 + 4 + 5) = 45
5x + 15 = 45
5x = 45 - 15
5x = 30
x = 6
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\(1+2+.......+x=45\)
\(\Rightarrow\frac{x\left(x+1\right)}{2}=45\)
\(\Rightarrow x\left(x+1\right)=90\)
mà \(90=9.10\)
\(\Rightarrow x=9\)
1 + 2 + 3 + 4 + ... + x = 45
(1 + x) × x : 2 = 45
(1 + x) × x = 45 × 2
(1 + x) × x = 90
(1 + x) × x = 10 × 9
=> x = 9
Vậy x = 9
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Bài 1:
\(A=\frac{1}{\left(1+2\right)}+\frac{1}{\left(1+2+3\right)}+\frac{1}{\left(1+2+3+4\right)}\)\(+\frac{1}{\left(1+2+3+4+5\right)}+...+\)\(\frac{1}{\left(1+2+3+...+10\right)}\)
\(A=\frac{1}{3}+\frac{1}{6}+....+\frac{1}{55}\)
\(A=2\left(\frac{1}{6}+\frac{1}{12}+....+\frac{1}{110}\right)\)
\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{10}-\frac{1}{11}\right)\)
\(A=2.\left(\frac{1}{2}-\frac{1}{11}\right)\)
\(A=\frac{9}{11}\)
Bài 2 :
2) Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15
Mẫu số = 11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17 lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x 17 = (1+27+125+729) x 13 x 15 x 17
\(\Rightarrow A< \frac{\left(1+27+125+729\right)\times11\times13\times15}{\left(1+27+125+729\right)\times13\times15\times17}\)
\(=\frac{11}{17}\)
\(=\frac{1111}{1717}=B\)
Vậy \(A=B\)
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(82 - 5.x) : 13 - 4 = 0
(82 - 5.x) : 13 = 0 + 4
(82 - 5.x) : 13 = 4
(82 - 5.x) = 4 . 13
(82 - 5.x) = 52
5.x = 82 - 52
5.x = 30
x = 30 : 5 = 6
(32 . 45) : 2 = (x + 70) : 14 - 40
720 = (x + 70) : 14 - 40
(x + 70) : 14 = 720 + 40
(x + 70) : 14 = 760
(x + 70) = 760 . 14
(x + 70) = 10640
x = 10640 - 70
x = 10570
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0,25 x 3 + 1 : 4 x 7
= 0,25 (3+7)
= 0,25 x 10
= 2,5
X x 1.2 + X x 1.8 = 45
X [1(2+8)] = 45
X [1 x 10] = 45
X x 10 = 45
X = 45 : 10
X = 4,5
\(5x+\left(1+2+3+4\right)=45\)
\(5x+10=45\)
\(5x=35\)
\(x=7\)
Vậy \(x=7\)
\(x+\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\left(x+4\right)=45\)
\(\Leftrightarrow5x+\left(1+2+3+4\right)=45\)
\(\Leftrightarrow5x+10=450\Rightarrow5x=440\Rightarrow x=88.\)