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TM
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6 tháng 4 2018
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 ~
3 tháng 4 2018
\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)
\(\left(x-2\right)\cdot\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)
\(\left(x-2\right)\cdot\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\cdot\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\cdot\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\cdot\left(\frac{3}{9}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\cdot\frac{2}{9}=\frac{16}{9}\)
\(x-2=\frac{16}{9}:\frac{2}{9}\)
\(x-2=\frac{16}{9}\cdot\frac{9}{2}\)
\(x-2=8\)
\(x=8+2\)
\(x=10\)
Vậy \(x=10\)
17 tháng 4 2020
\(\left(x-2\right)\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)=\)\(=\frac{16}{9}\)
\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\left(\frac{2}{9}\right)=\frac{16}{9}\)
2(x-2)=16
x-2=8
x=10
16 tháng 2 2017
\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x+2}{42} +\frac{x+2}{56}+\frac{x+2}{72}=\frac{16}{9}\)
\(\Rightarrow x-2\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)=\frac{16}{9}\)
\(\Rightarrow x-2\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+\frac{1}{5}-...+\frac{1}{8}-\frac{1}{8}+\frac{1}{9}\right)=\frac{16}{9}\)
\(\Rightarrow x-2\left(\frac{1}{3}+\frac{1}{9}\right)=\frac{16}{9}\)
\(\Rightarrow\left(x-2\right)\frac{4}{9}=\frac{16}{9}\)
\(\Rightarrow x-2=4\)
\(\Rightarrow x=6\)
28 tháng 5 2016
=> x-2.(1/12+1/20+1/30+1/42+1/56+1/72)=16/9
Đặt : Sáng = 1/12+1/20+1/30+1/42+1/56+1/72
=> Sáng = 1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9
=> Sáng = 1.(1/3-1/4+1/4-1/5+...+1/8-1/9
=> Sáng = 91.(1/3-1/9)
=> Sáng = 2/9
Thay Sáng vô biểu thức 1/12+1/20+1/30+1/42+1/56+1/72
Ta được :
x-2.2/9=16/9
giờ thì tự làm nha
28 tháng 5 2016
=> x-2.(1/12+1/20+1/30+1/42+1/56+1/72)=16/9
Đặt : Sáng = 1/12+1/20+1/30+1/42+1/56+1/72
=> Sáng = 1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9
=> Sáng = 1.(1/3-1/4+1/4-1/5+...+1/8-1/9
=> Sáng = 91.(1/3-1/9)
=> Sáng = 2/9
Thay Sáng vô biểu thức 1/12+1/20+1/30+1/42+1/56+1/72
Ta được :
x-2.2/9=16/9
giờ thì tự làm nha
Ai k mk mk k lại
21 tháng 3 2018
x-2/12 + x-2/20+....+x-2/72
=x-2/3.4+ x-2/ 4.5+...+x-2/8.9
=(x-2).1/3.4.1+(x-2).1/4.5.1+......+(x-2).1/8.9.1
=x-2/1(1/3.4+1/4.5+....+1/8.9)
=x-2(1/3 -1/4 +1/4 -1/5+...+1/8-1/9)
=x-2(1/3-1/9)
=(x-2).2/9
=2x-4/9
IA
28 tháng 2 2020
\(\left(x-2011\right)\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)
\(\left(x-2011\right)\cdot\frac{2}{9}=\frac{16}{9}\)
\(x-2011=8\)
\(x=2019\)
LT
28 tháng 2 2020
\(\frac{x-2011}{12}+\frac{x-2011}{20}+\frac{x-2011}{30}+\frac{x-2011}{42}+\frac{x-2011}{56}+\frac{x-2011}{72}=\frac{16}{9}\)
\(\left(x-2011\right)\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)
\(\left(x-2011\right)\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)=\frac{16}{9}\)
\(\left(x-2011\right)\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2011\right)\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2011\right)\frac{2}{9}=\frac{16}{9}\)
\(x-2011=8\Rightarrow x=2019\)
\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+..+\frac{x-2}{72}=\frac{16}{9}\)
\(\Rightarrow\left(x-2\right).\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{72}\right)=\frac{16}{9}\)
\(\Rightarrow\left(x-2\right).\left(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}\right)=\frac{16}{9}\)
\(\Rightarrow\left(x-2\right).\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\Rightarrow\left(x-2\right).\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\Rightarrow x-2=0\Rightarrow x=2\)
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