\(3^x+3^{x+1}+3^{x+2}=117\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
=> 3^x-2 . (3^2+3+1) = 117
=> 3^x-2 . 13 = 117
=> 3^x-2 = 117 : 13 = 9
=> 3^x-2 = 3^2
=> x-2 = 2
=> x = 4
Vậy x = 4
Tk mk nha
![](https://rs.olm.vn/images/avt/0.png?1311)
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 \(A=B\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
=> 3^x . (1+3+3^2) = 117
=> 3^x . 13 = 117
=> 3^x = 117 : 13 = 9
=> 3^x = 3^2
=> x = 2
Vậy x = 2
Tk mk nha
3x + 3x+1 +3x+2 = 117
=> 3x + 3x . 3 + 3x . 9 = 117
=> 3x ( 1 + 3 + 9) = 117
=> 3x . 13 = 117
=> 3x = 9
=> x = 2
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3^x+3^{x+1}+3^{x+2}=117\)
\(\Rightarrow3^x+3^x.3+3^x.3^2=117\)
\(\Rightarrow3^x.\left(1+3+3^2\right)=117\)
\(\Rightarrow3^x.13=117\)
\(\Rightarrow3^x=9\)
\(\Rightarrow3^x=3^2\)
\(\Rightarrow x=2\)
Vậy \(x=2\)
\(\Rightarrow3^x\left(1+3+3^2\right)=117\)
\(\Rightarrow3^x.13=117\)
\(\Rightarrow3^x=9\)
=>x = 2
Vây x = 2
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1)\(A=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{55}=2\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=2.\left(\frac{1}{2}-\frac{1}{11}\right)=\frac{9}{11}\)
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
=> \(A
![](https://rs.olm.vn/images/avt/0.png?1311)
3x+3x+1+3x+2=117
=> 3x.(1+3+32)=117
=> 3x.(1+3+9)=117
=> 3x.13=117
=> 3x=117:13
=> 3x=9
=> 3x=32
=> x=2
3x+3x+1+3x+2=117
=> 3x.(1+3+32)=117
=> 3x.(1+3+9)=117
=> 3x.13=117
=> 3x=117:13
=> 3x=9
=> 3x=32
=> x= 2
tick nha
3^x + 3^x+1 + 3^x+2=117
3^x.(1+3+3^2)=117
3^x.13=117
3^x=117:13
3^x=9
Ta có:9=3^2
Vậy x=2
=>3x+x+x+1+2=117
=>33x+3=117
=>