a. \(\frac{x+1}{2}=\frac{8}{x+1}\)

\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=8.2\)

\(\Leftrightarrow\left(x+1\right)^2=16\)

\(\Leftrightarrow\left(x+1\right)^2=2^4\)

\(\Leftrightarrow\left(x+1\right)=2^2\)

\(\Leftrightarrow\left(x+1\right)=4\)

\(\Leftrightarrow x=4-1=3\)

b. \(x:\left(9\frac{1}{2}-\frac{3}{2}\right)=\frac{0,4+\frac{2}{9}-\frac{2}{11}}{1,6+\frac{8}{9}-\frac{8}{11}}\)

\(\Leftrightarrow x:\left(\frac{10}{2}-\frac{3}{2}\right)=\frac{0,4+0,2-0,18}{1,6+0,8-0,72}\)

\(\Leftrightarrow x:\frac{7}{2}=\frac{\frac{21}{50}}{\frac{42}{25}}\)

\(\Leftrightarrow x=\frac{\frac{21}{50}}{\frac{42}{25}}.\frac{7}{2}\Leftrightarrow x=\frac{1}{4}.\frac{7}{2}=\frac{7}{8}\)

a )  \(\frac{x+1}{2}=\frac{8}{x+1}\)

\(\Rightarrow\left(x+1\right).\left(x+1\right)=2.8\)

\(\Rightarrow\left(x+1\right)^2=16\)

\(\Rightarrow\orbr{\begin{cases}x+1=4\\x+1=-4\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=4-1\\x=-4-1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=3\\x=-5\end{cases}}\)

Dấu " \(\orbr{\begin{cases}\\\end{cases}}\)là hoặc nha !!! 

a)\(\frac{x+1}{2}=\frac{8}{x+1}\)

\(\Rightarrow\left(x+1\right)^2=8\times2=16\)

\(\Rightarrow\left(x+1\right)^2=4^2\)

\(\Rightarrow x+1=4\)

\(\Rightarrow x=4-1=3\)

b)tớ ko biết làm . ~ sorry~

~chuk bn hok giỏi~

\(\frac{x+1}{9}+\frac{x+2}{8}+\frac{x+3}{7}+...+\frac{x+9}{1}=-9\)

\(\left(\frac{x+1}{9}+1\right)+\left(\frac{x+2}{8}+1\right)+\left(\frac{x+3}{7}+1\right)+...+\left(\frac{x+9}{1}+1\right)=0\)

\(\frac{x+10}{9}+\frac{x+10}{8}+\frac{x+10}{7}+...+\frac{x+10}{1}=0\)

\(\left(x+10\right).\left(\frac{1}{9}+\frac{1}{8}+\frac{1}{7}+...+1\right)=0\)

vì \(\frac{1}{9}+\frac{1}{8}+\frac{1}{7}+...+1\ne0\)

\(\Rightarrow x+10=0\)

\(\Rightarrow x=-10\)

SKT_NTT làm đúng ùi -_- 100 %

\(\left(\frac{x+1}{9}+1\right)+\left(\frac{x+2}{8}+1\right)+...+\left(\frac{x+9}{1}+1\right)=-9+9\)

\(\Rightarrow\frac{x+10}{9}+\frac{x+10}{8}+...+\frac{x+10}{1}\) =

x:(19:2-3:2)=(2:5+2:9-2:11):(8:5+8:9-8:11)

x:8=2(1:5+1:9-1:11):8(1:5+1:9-1:11)

x:8=1:6

x=(1:6)8

x=4:3

vì không viết được phân số nên mình đành dùng dấu chia thông cảm

Dùng tính chất dãy tỉ số bằng nhau

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Xét vế phải

\(\frac{1}{9}+\frac{2}{8}+\frac{3}{7}+\frac{4}{6}+\frac{5}{5}+\frac{6}{4}+\frac{7}{3}+\frac{8}{2}+\frac{9}{1}\)
\(=\frac{1}{9}+\frac{2}{8}+\frac{3}{7}+\frac{4}{6}+\frac{5}{5}+\frac{6}{4}+\frac{7}{3}+\frac{8}{2}+9\)

\(=\frac{1}{9}+\frac{2}{8}+\frac{3}{7}+\frac{4}{6}+\frac{5}{5}+\frac{6}{4}+\frac{7}{3}+\frac{8}{2}+\left(1+1+...+1\right)\)

\(=\left(1+\frac{1}{9}\right)+\left(1+\frac{2}{8}\right)+\left(1+\frac{3}{7}\right)+\left(1+\frac{4}{6}\right)+\left(1+\frac{5}{5}\right)+\left(1+\frac{6}{4}\right)+\left(1+\frac{7}{3}\right)+\left(1+\frac{8}{2}\right)+1\)\(=\frac{10}{9}+\frac{10}{8}+\frac{10}{7}+\frac{10}{6}+\frac{10}{5}+\frac{10}{4}+\frac{10}{3}+\frac{10}{2}+\frac{10}{10}\)

\(=10\times\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\right)\)

Thay vào bài ,ta được:

\(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\right)\times x=10\times\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\right)\)\(\Rightarrow x=10\)

Vậy x=10

chúc bạn học tốt

a) x = 3 hoặc -5

b) 2

a ) (x+1)²=16

=>x+1=4    (vì x là số tự nhiên nên x+1=-4 là ko thỏa mãn)

=>x=3

b)x=2 ( cậu quy đồng rồi tự giải , có gì ko hiểu thì hỏi riêng mình )

C =22−3 x 4− x =12−3 x +104− x =3(4− x )4− x +104− x =3+104− x ... +199.100 ). x =201251 +201252 +. .... =12√3 (4+2√3√3+1+4−2√3√3−1 )=12√3 .4√3−4+6−2√3+4√3+4−6−2√3(√3−1)(√3+1).

\(\frac{1}{4}+\frac{8}{9}< \frac{x}{36}< 1-\frac{3}{8}+\frac{5}{6}\)

\(=\frac{41}{36}< \frac{x}{36}< \frac{35}{24}\)

=>\(x=35< x< 41\)

\(\left(-\frac{2}{3}:-\frac{1}{3}\right).\left(-\frac{9}{2}\right)-\frac{1}{4}< \frac{x}{8}< -\frac{1}{2}.\frac{3}{4}:\frac{1}{8}+1\)

\(2.\left(-\frac{9}{2}\right)-\frac{1}{4}< \frac{x}{8}< \left(-3\right)+1\)

\(\left(-9\right)-\frac{1}{4}< \frac{x}{8}< \left(-2\right)\)

\(\left(-\frac{37}{4}\right)< \frac{x}{8}< \left(-2\right)\)

\(-\frac{74}{8}< \frac{x}{8}< -\frac{16}{8}\)

            Vậy -74<x<-16

\(\frac{x-1}{9}+\frac{x-2}{8}+\frac{x-3}{7}=\frac{x-4}{6}\)

\(\frac{x-1}{9}+\frac{x-2}{8}+\frac{x-3}{7}-\frac{x-4}{6}=0\)

\(\frac{56.\left(x-1\right)}{504}+\frac{63.\left(x-2\right)}{504}+\frac{72.\left(x-3\right)}{504}-\frac{84.\left(x-4\right)}{504}=0\)

\(\frac{56x-56}{504}+\frac{63x-126}{504}+\frac{72x-216}{504}-\frac{84x-336}{504}=0\)

\(\Rightarrow56x-56+63x-126+72x-216-84x+336=0\)

\(\Rightarrow107x-62=0\)

\(\Rightarrow107x=62\)

\(\Rightarrow x=\frac{62}{107}\)

vay \(x=\frac{62}{107}\)

\(\frac{4}{5}-\left|3-x\right|=\frac{1}{4}\)

\(\Rightarrow\left|3-x\right|=\frac{4}{5}-\frac{1}{4}\)

\(\Rightarrow\left|3-x\right|=\frac{11}{20}\)

\(\Rightarrow\hept{\begin{cases}3-x=\frac{11}{20}\\3-x=-\frac{11}{20}\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x=\frac{49}{20}\\x=\frac{71}{20}\end{cases}}\)

\(\frac{8}{9}:x^2+\frac{1}{9}=1\)

\(\Rightarrow\frac{8}{9}:x^2+\frac{1}{9}=\frac{9}{9}\)

\(\Rightarrow\frac{8}{9}:x^2=\frac{9}{9}-\frac{1}{9}\)

\(\Rightarrow\frac{8}{9}:x^2=\frac{8}{9}\)

\(\Rightarrow x^2=\frac{8}{9}:\frac{8}{9}\)

\(\Rightarrow x^2=1\)

\(\Rightarrow x^2=1^2\)

\(\Rightarrow x=1\)

Thêm:

\(\frac{4}{5}+\frac{3}{4}.x\frac{5}{2}\)

\(x-\frac{1}{2}=-\frac{5}{2}\)