Question

\(\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+...+\frac{2}{19\cdot21}-x+4+\frac{221}{231}=\frac{7}{3}\)

ai nhanh tick ( giải đầy đủ nha )

Answer 1

=> 1/11 - 1/13 + 1/13 - 1/15 + ..... + 1/19 - 1/21 - x + 4 + 221/231 = 7/3

=> 1/11 - 1/21 - x + 4 + 221/231 = 7/3

=> 2099/420 - x = 7/3

=> x = 2099/420 - 7/3 = 373/140

Tk mk nha

Answer 2

Bài làm

\(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\Leftrightarrow2\left(\frac{1}{11.13}+\frac{1}{13.15}+...+\frac{1}{19.21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\Leftrightarrow2\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\Leftrightarrow2\left(\frac{1}{11}-\frac{1}{21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\Leftrightarrow2.\frac{10}{231}-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\Leftrightarrow\frac{20}{231}-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\Leftrightarrow\frac{20}{231}-x+\frac{924}{231}+\frac{221}{231}=\frac{539}{231}\)

\(\Leftrightarrow\frac{20}{231}-x+\frac{924}{231}=\frac{539}{231}-\frac{221}{231}\)

\(\Leftrightarrow\frac{20}{231}-x+\frac{924}{231}=\frac{318}{231}\)

\(\Leftrightarrow\frac{20}{231}-x=\frac{318}{231}-\frac{924}{231}\)

\(\Leftrightarrow\frac{20}{231}-x=-\frac{606}{231}\)

\(\Leftrightarrow x=\frac{20}{231}-\frac{606}{231}\)

\(\Leftrightarrow x=-\frac{586}{231}\)

Vậy \(\Leftrightarrow=-\frac{586}{231}\)

Answer 3

ta có : 2/11*15 +2/13*15+...+2/19*21 - x +4+221/231=7/3

=>(1/11 -1/13 + 1/13-1/15+...+1/19 - 1/21)-x+4 +221/231=7/3

<=>(1/11 - 1/21)-x+4 + 221/231=7/3

<=>10/231 -  x+4 +221/231 =7/3

<=>1-x +4=7/3

<=>x+4=1-7/3

<=>x+4=-4/3

<=>x=-4/3-4

<=>x=-16/3

vậy x=-16/3