tìm x
x+x/2+x/6+x/12+x/20+x/30+x/42+x/56=28
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ND
0
TM
0
HA
4
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 ~
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
NV
0
CN
0
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
MT
4
3 tháng 4 2018
\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+..+\frac{x-2}{72}=\frac{16}{9}\)
\(\Rightarrow\left(x-2\right).\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{72}\right)=\frac{16}{9}\)
\(\Rightarrow\left(x-2\right).\left(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}\right)=\frac{16}{9}\)
\(\Rightarrow\left(x-2\right).\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\Rightarrow\left(x-2\right).\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\Rightarrow x-2=0\Rightarrow x=2\)
Ghi rõ đề ra, VP là bao nhiêu?
Biến đổi VT:
\(x+\frac{x}{2}+\frac{x}{6}+\frac{x}{12}+\frac{x}{20}+\frac{x}{30}+\frac{x}{42}+\frac{x}{56}\)
\(=x\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{6.7}+\frac{1}{7.8}\right)\)
\(=x\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\right)\)
\(=x\left(2-\frac{1}{8}\right)\)
\(=x.\frac{15}{8}\)
\(x+\frac{x}{2}+\frac{x}{6}+\frac{x}{12}+\frac{x}{20}+\frac{x}{30}+\frac{x}{42}+\frac{x}{56}=28\)
\(\Leftrightarrow x\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\right)=28\)
\(\Leftrightarrow x\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\right)=28\)
\(\Leftrightarrow x\left(1+1-\frac{1}{8}\right)=28\)
\(\Leftrightarrow x.\frac{15}{8}=28\)
\(\Leftrightarrow x=\frac{224}{15}\)