Ta có :
\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)
\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)
\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)=\frac{16}{9}\)
\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\Leftrightarrow\)\(\left(x-2\right).\frac{2}{9}=\frac{16}{9}\)
\(\Leftrightarrow\)\(x-2=\frac{16}{9}:\frac{2}{9}\)
\(\Leftrightarrow\)\(x-2=\frac{16}{9}.\frac{9}{2}\)
\(\Leftrightarrow\)\(x-2=\frac{8}{1}.\frac{1}{1}\)
\(\Leftrightarrow\)\(x-2=8\)
\(\Leftrightarrow\)\(x=8+2\)
\(\Leftrightarrow\)\(x=10\)
Vậy \(x=10\)
Chúc bạn học tốt ~
(x+x+x+x+x+x)-(2/12+2/20+2/30+2/42+2/56+2/72)=16/9
6x-4/9=16/9
6x=20/9=>x=20/7
Trả lời
\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)
\(x-2\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{21}{56}+\frac{1}{72}\right)=\frac{16}{9}\)
\(x-2\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)=\frac{16}{9}\)
\(x-2\cdot\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(x-2\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\Rightarrow\left(x-2\right)\cdot\frac{2}{9}=\frac{16}{9}\)
\(\)\(\Rightarrow2\left(x-2\right)=16\)
\(\Rightarrow x-2=16:2\)
\(\Rightarrow x-2=8\)
\(\Rightarrow x=8+2\)
\(\Rightarrow x=10\)
Vậy x=10
(x-2)(1/12+1/20+1/30+1/42+1/56+1/72)=16/9
(x-2)(1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9)=16/9
(x-2)(1/3-1/9)=16/9
(x-2).2/9=16/9
suy ra x-2=16/9:2/9
x-2=8
suy ra x=10