\(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{x\left(x+2\right)}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{x}-\dfrac{1}{x+2}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{x+2}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{x+2-2}{2\left(x+2\right)}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{x}{2x+4}=\dfrac{4}{9}\)

\(\Rightarrow9x=8x+16\)

\(\Rightarrow x=16\)

Vậy x = 16

tại sao lại =1/2

\(S=\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{x\left(x+2\right)}=\frac{4}{9}\)
\(S=\frac{4-2}{2.4}+\frac{6-2}{4.6}+...+\frac{\left(x+2\right)-x}{x\left(x+2\right)}=\frac{4}{9}\)
\(S=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{4}{9}\)
\(S=\frac{1}{2}-\frac{1}{x+2}=\frac{4}{9}\)
\(\Rightarrow\frac{1}{x+2}=\frac{1}{2}-\frac{4}{9}=\frac{1}{18}\)
\(\Rightarrow x+2=18\Rightarrow x=18-2=16\)
Vậy x=16

\(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+...+\frac{2}{x\left(x+2\right)}=\frac{4}{9}\)

\(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{4}{9}\)

\(\frac{1}{2}-\frac{1}{x+2}=\frac{4}{9}\)

\(\frac{1}{x+2}=\frac{1}{2}-\frac{4}{9}\)

\(\frac{1}{x+2}=\frac{1}{18}\)

\(\Leftrightarrow x+2=18\)

=> x = 18 - 2

x = 16

Vậy x =16

\(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{x\left(x+2\right)}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{x}-\dfrac{1}{x+2}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{x+2}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{x+2-2}{2\left(x+2\right)}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{x}{2x+4}=\dfrac{4}{9}\)

\(\Rightarrow9x=8x+16\)

\(\Rightarrow x=16\)

Vậy x = 16

2/2.4+2/4.6+......+2/x.(x+2)=4/9

1/2-1/4+1/4-1/6+....+1/x-1/x+2=4/9

1/2-1/x+2=4/9

1/x+2=1/2-4/9

1/x+2=1/18

=>x+2=18

x=18-2=16

\(\frac{2}{2.4}+\frac{2}{4.6}+....+\frac{2}{x\left(x+2\right)}=\frac{4}{9}\)

<=> \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{x}-\frac{1}{x+2}=\frac{4}{9}\)

<=>  \(\frac{1}{2}-\frac{1}{x+2}=\frac{4}{9}\)

<=> \(\frac{1}{x+2}=\frac{1}{18}\)

=>  \(x+2=18\)

<=>  \(x=16\)

Vậy...

bạn tk mình một lần cho mình biết đi mình chưa được ai tk lần nào

Nhưng bn phải trả lời chứ

\(\dfrac{4}{2\cdot4}+\dfrac{4}{4\cdot6}+\dfrac{4}{6\cdot8}+...+\dfrac{4}{x\left(x+2\right)}=\dfrac{2011}{2013}\)

\(\Leftrightarrow2\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+...+\dfrac{2}{x\left(x+2\right)}\right)=\dfrac{2011}{2013}\)

\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{x}-\dfrac{1}{x-2}=\dfrac{2011}{4026}\)

\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{x-2}=\dfrac{2011}{4026}\)\(\Leftrightarrow\dfrac{1}{x-2}=\dfrac{1}{2013}\)

\(\Rightarrow x-2=2013\Rightarrow x=2015\)

\(a,\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)

\(\frac{11}{15}x=\frac{2}{5}\)

\(x=\frac{6}{11}\)

b,\(\left(2x-3\right).\left(6-2x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}2x-3=0\\6-2x=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{3}{2}\\x=3\end{cases}}\)

Vậy

a) \(\left(x+1\right)^2=64\Leftrightarrow\left|x+1\right|=8\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x+1=8\\x+1=-8\end{array}\right.\) \(\Leftrightarrow\left[\begin{array}{nghiempt}x=7\\x=-9\end{array}\right.\)

b) \(\frac{9}{2.4}+\frac{9}{4.6}+...+\frac{9}{96.98}+\frac{9}{98.100}=\frac{9}{4}\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{48.49}+\frac{1}{49.50}\right)\)

\(=\frac{9}{4}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{48}-\frac{1}{49}+\frac{1}{49}-\frac{1}{50}\right)\)

\(=\frac{9}{4}\left(1-\frac{1}{50}\right)=\frac{441}{200}\)

a)(x+1)²=64

x + 1      = 8

x            = 8 - 1

x            = 7