Ta có : \(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+...+\frac{1}{x\left(x+3\right):2}=\frac{9}{14}\)

\(\Rightarrow2\left(\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+...+\frac{1}{x\left(x+3\right)}\right)=\frac{9}{14}\)

\(\Rightarrow2.\frac{1}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{x\left(x+3\right)}\right)=\frac{9}{14}\)

\(\Rightarrow\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{9}{14}\)

\(\Rightarrow1-\frac{1}{x+3}=\frac{27}{28}\)

\(\Rightarrow\frac{1}{x+3}=\frac{1}{28}\)

=> x + 3 = 28

=> x  = 25 

a)

(x*211)+(1+2+...+211)=23632

(x*211)+22366=23632

x*211=23632-22366

x*211=1266

x=1266:211

x=6

Vậy x=6

2/3 = 2 x 4/ 3 x 4 =8/12

8/14 = 8 : 2/ 14 : 2 =4/7

5/9 = 5 x3/ 9 x 3 =15/37

35/ 40 = 35 : 5/ 40 : 5=7/8

x² -3² = 6x -x² -18 +3x 

(x -3 )(x+3 ) =9x -x² - 9

 x² +3x-3x- 9 =9x - x² -9

x² - x ² -9x = -9 +9 

-9 x = 0

=> x = 0

\(C=5\frac{9}{10}:\frac{3}{2}-\left(2\frac{1}{3}.4\frac{1}{2}-2.2\frac{1}{3}\right):\frac{7}{4}\)

\(=\frac{59}{10}:\frac{3}{2}-\left(\frac{7}{3}.\frac{9}{2}-2.\frac{7}{3}\right):\frac{7}{4}\)

\(=\frac{59}{15}-\left[\frac{7}{3}\left(\frac{9}{2}-2\right)\right]:\frac{7}{4}\)

\(=\frac{59}{15}-\frac{35}{6}:\frac{7}{4}\)

\(=\frac{59}{15}-\frac{10}{3}\)

\(=\frac{9}{15}=\frac{3}{5}\)

\(\cdot62,87+35,14+4,13+8,35+4,86+5,65\)

\(=\left(62,87+4,13\right)+\left(35,14+4,86\right)+\left(8,35+5,65\right)\)

\(=67+40+14\)

\(=121\)

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\(\hept{\begin{cases}\frac{x^2}{16}=-\frac{9}{14}\\\frac{2y^2}{50}=-\frac{9}{14}\\\frac{z}{6}=-\frac{9}{14}\end{cases}}< =>\hept{\begin{cases}14x^2=-144\left(voli\right)\\28y^2=-450\left(voli\right)\\14z=-54< =>z=-\frac{54}{14}\end{cases}}\)

Bài 1:

a) \(x.\dfrac{3}{4}=\dfrac{9}{14}\)

\(\Rightarrow x=\dfrac{9}{14}:\dfrac{3}{4}\)

\(\Rightarrow x=\dfrac{6}{7}\)

b) \(x:\dfrac{5}{9}=\dfrac{3}{10}\)

\(\Rightarrow x=\dfrac{3}{10}.\dfrac{5}{9}\)

\(\Rightarrow x=\dfrac{1}{6}\)

help me

a: Sửa đề: \(3^{2x-1}+2\cdot9^{x-1}=405\)

=>\(3^{2x-1}+2\cdot3^{2x-2}=305\)

=>\(3^{2x-2+1}+2\cdot3^{2x-2}=405\)

=>\(5\cdot3^{2x-2}=405\)

=>\(3^{2x-2}=81=3^4\)

=>2x-2=4

=>2x=6

=>x=3

b: Ta có: \(\frac35\left(3x^3-\frac89\right)-\frac12\left(\frac32-1\right)=-\frac14\)

=>\(\frac35\left(3x^3-\frac89\right)-\frac12\cdot\frac12=-\frac14\)

=>\(\frac35\left(3x^3-\frac89\right)=-\frac14+\frac14=0\)

=>\(3x^3-\frac89=0\)

=>\(3x^3=\frac89\)

=>\(x^3=\frac{8}{27}=\left(\frac23\right)^3\)

=>\(x=\frac23\)

c: Ta có: \(\left(\frac13\right)^{x-1}+5\cdot\left(\frac13\right)^{x+1}=\frac{14}{9^3}\)

=>\(\left(\frac13\right)^{x-1}+5\cdot\left(\frac13\right)^{x-1}\cdot\frac19=\frac{14}{3^6}\)

=>\(\left(\frac13\right)^{x-1}\left(1+\frac59\right)=\frac{14}{3^6}\)

=>\(\left(\frac13\right)^{x-1}=\frac{14}{3^6}:\frac{14}{9}=\frac{9}{3^6}=\frac{1}{3^4}\)

=>x-1=4

=>x=5