729:(y x 9 )=27
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![](https://rs.olm.vn/images/avt/0.png?1311)
`Answer:`
\(\left(x+\frac{1}{3}\right)+\left(x+\frac{1}{9}\right)+\left(x+\frac{1}{27}\right)+...+\left(x+\frac{1}{729}\right)=\frac{4209}{729}\)
\(\Leftrightarrow\left(x+\frac{1}{3}\right)+\left(x+\frac{1}{3^2}\right)+\left(x+\frac{1}{3^3}\right)+...+\left(x+\frac{1}{3^6}\right)=\frac{4209}{729}\)
\(\Leftrightarrow6x+\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^6}\right)=\frac{4209}{729}\text{(*)}\)
Đặt \(N=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^6}\)
\(\Leftrightarrow3N=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^5}\)
\(\Leftrightarrow3N-N=\left(1+\frac{1}{3}+\frac{1}{3^2}+..+\frac{1}{3^5}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^6}\right)\)
\(\Leftrightarrow2N=1-\frac{1}{3^6}\)
\(\Leftrightarrow2N=\frac{728}{729}\)
\(\Leftrightarrow N=\frac{364}{729}\)
\(\text{(*)}\Leftrightarrow6x+\frac{364}{729}=\frac{4209}{729}\)
\(\Leftrightarrow6x=\frac{3845}{729}\)
\(\Leftrightarrow x=\frac{3845}{4374}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{x^3}{27}+\dfrac{x^6}{729}-x^9=\dfrac{x}{3}+\dfrac{x}{3}-\dfrac{3x^9}{3}=\dfrac{2x-3x^9}{3}=\dfrac{x\left(2-3x^8\right)}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{x^7}{81}=27\)
=> x7 = 27.81
=> x7 = 33.34
=> x7 = 37
=> x = 3
Vậy x = 3
b) \(\frac{x^8}{9}=729\)
=> x8 = 729.9
=> x8 = 36.32
=> x8 = 38 = (-3)8
=> \(x\in\left\{3;-3\right\}\)
Vậy \(x\in\left\{3;-3\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
x^7/81 = 27 x^8/9 = 729
x^7 : 81= 27 x^8 : 9 = 729
x^7 =27.81 x^8 = 729.9
x^7 =2187 x^8 =6561
x^7 = 3^7 x^8 = 3^8
=> x =3 => x = 3
\(\frac{x^7}{81}=27\Rightarrow x^7=27.81=2187\Rightarrow x=\sqrt[7]{2187}=3\)
\(\frac{x^8}{9}=729\Rightarrow x^8=729.9=6561\Rightarrow x=\sqrt[8]{6561}=3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\dfrac{3\cdot7\cdot3^4\cdot3^6+3^6\cdot3^4\cdot3^3}{3^2\cdot3^4\cdot2\cdot3^{12}\cdot13+3^2\cdot2\cdot3^3\cdot2\cdot3^4\cdot2\cdot3^2+723\cdot729}\)
\(=\dfrac{3^{11}\cdot7+3^{13}}{3^{18}\cdot26+3^{11}\cdot8+3^7\cdot241}\)
\(=\dfrac{3^{11}\left(7+9\right)}{3^7\left(3^{11}\cdot26+3^4\cdot8+241\right)}=\dfrac{3^7\cdot16}{17\cdot101\cdot2683}\)
729 : ( y x 9 ) = 27
y x 9 = 729 : 27
y x 9 = 27
y = 27 : 9
y = 3
Chúc bạn học tốt >w<
\(729:\left(y\times9\right)=27\)
\(y\times9=729:27\)
\(y\times9=27\)
\(y=27:9\)
\(y=3\)
Vậy \(y=3\)