54444

\(b.\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)

\(\Leftrightarrow\frac{35+9}{105}< \frac{x}{210}< \frac{60+63+35}{105}\)

\(\Leftrightarrow\frac{44}{105}< \frac{x}{210}< \frac{158}{105}\)

\(\Leftrightarrow\frac{88}{210}< \frac{x}{210}< \frac{316}{210}\)

Suy ra \(x\in\left\{89;90;100;...;313;314;315\right\}\)

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

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

\(\Leftrightarrow\frac{1}{11}-\frac{1}{21}-x+\frac{221}{231}=\frac{4}{3}\)

\(\Leftrightarrow\frac{21-11-231x+221}{231}=\frac{308}{231}\)

\(\Leftrightarrow-231x=308-21+11-221\)

\(\Leftrightarrow-231x=77\)

\(\Leftrightarrow x=-\frac{77}{231}=-\frac{1}{3}\)

^^

mk chỉ làm được câu a thôi : 

a) gọi A= \(\frac{2}{11.13}+\frac{2}{13.15}+......+\frac{2}{19.21}\)

A= \(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+......+\frac{1}{19}-\frac{1}{21}\)

     \(\frac{1}{11}-\frac{1}{21}\)

       \(\frac{21}{231}-\frac{11}{231}\)= \(\frac{10}{231}\)

\(\Rightarrow\frac{10}{231}.462-[2,04:\left(x+1,05\right)]:0,12=19\)

20,08 - \([2,04:\left(x+1,05\right)]:0,12=19\)

\(.........\)

\(\Leftrightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right).462-\frac{17}{x+1,05}=19.\)

\(\Leftrightarrow\left(\frac{1}{11}-\frac{1}{21}\right)462-\frac{17}{x+1,05}=19\)

\(\Leftrightarrow20-\frac{17}{x+1,05}=19\)

\(\Leftrightarrow1-\frac{17}{x+1,05}=0\)

\(\Leftrightarrow x+1,05=17\)

\(\Leftrightarrow x=15,95\)

Đặt  \(A=\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\)

      \(A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+...+\frac{1}{19}-\frac{1}{21}\)

       \(A=\frac{1}{11}-\frac{1}{21}=\frac{10}{231}\)

thay A vào ta được:

\(\frac{10}{231}-x+\frac{23}{231}=\frac{5}{77}\) 

\(x+\frac{23}{231}=\frac{10}{231}-\frac{5}{77}=-\frac{5}{231}\)

\(x=-\frac{5}{231}-\frac{23}{231}=\frac{-4}{33}\)

\(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}-x+\frac{23}{231}=\frac{5}{77}\)\(\frac{5}{77}\)

=>\(\frac{1}{11}-\frac{1}{21}-x+\frac{23}{231}=\frac{5}{77}\)

=>\(\frac{10}{231}+\frac{23}{231}-x=\frac{5}{77}\)

=>\(\frac{33}{231}-x=\frac{5}{77}\)

=>\(\frac{1}{7}-x=\frac{5}{77}\)

=>\(\frac{11}{77}-x=\frac{5}{77}\)

=>\(x=\frac{11}{77}-\frac{5}{77}=\frac{6}{77}\)

Vậy \(x=\frac{6}{77}\)

bạn nguyệt hằng giải sai rồi 1,5 chứ ko phải 15

a, (x+1)+(x+4)+(x+7)+...+(x+28)=155

=>x.10+(1+4+7+...+28)              =155

=>    x.10+145                            =155

=>           x.10                              = 155-145

=>           x.10                              = 10

=>            x                                  =10:10

=>           x                                    =1

Vậy x= 1