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a) \(\left(x-\frac{1}{2}\right).\frac{1}{3}+\frac{5}{7}=9\frac{5}{7}\)
\(\left(x-\frac{1}{2}\right).\frac{1}{3}=9\frac{5}{7}-\frac{5}{7}\)
\(x-\frac{1}{2}=9:\frac{1}{3}\)
\(x=27+\frac{1}{2}\)
\(x=\frac{55}{2}\)
b)\(\frac{1}{2}.x+150\%.x=2014\)
\(\left(\frac{1}{2}+150\%\right)x=2014\)
\(2x=2014\)
\(x=2014:2\)
\(x=1007\)
c) \(2-\left|\frac{3}{4}\right|=\frac{7}{2}\)???????
và bài này nữa
tính nhanh
a, \(5\frac{7}{5}\cdot4\frac{2}{7}+5\frac{5}{7}\cdot4\frac{2}{7}\)
b, \(b,\frac{-7}{11}\cdot\frac{4}{19}+\frac{-7}{19}\cdot\frac{7}{11}+2\frac{7}{19}\)
cảm ơn giúp nhiều
b)
\(x-2.\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)=\frac{16}{9}\)
\(x-2\cdot\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(x-2=\frac{16}{9}:\left(\frac{1}{3}-\frac{1}{9}\right)\)
\(x-2=8\)
=> x = 10
a)
\(A=\frac{1}{2}.\frac{2}{3}\cdot\frac{3}{4}\cdot\cdot\cdot\frac{2013}{2014}\cdot\frac{2014}{2015}\cdot\frac{2015}{2016}\)
\(A=\frac{1}{2016}\)
a)\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\Leftrightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\Leftrightarrow x\left(x-1\right)^{x+2}\left(x-2\right)=0\)
Do đó \(x\in\left\{0;1;2\right\}\)
b)
\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot...\cdot\frac{31}{64}=2^x\Leftrightarrow\frac{1\cdot2\cdot3\cdot...\cdot31}{4\cdot6\cdot8\cdot...\cdot64}=2^x\Leftrightarrow\frac{31!}{\left(2\cdot2\right)\cdot\left(2\cdot3\right)\cdot\left(2\cdot4\right)\cdot...\cdot\left(2\cdot31\right)\cdot64}=2^x\)
\(\frac{31!}{2^{30}\cdot31!\cdot2^6}=2^x\Leftrightarrow\frac{1}{2^{36}}=2^x\Leftrightarrow2^{-36}=2^x\Rightarrow x=-36\)
\(a,\frac{x-1}{12}=\frac{75}{x-1}\)
\(\Rightarrow\left(x-1\right)\left(x-1\right)=12\cdot75\)
\(\Rightarrow\left(x-1\right)^2=900\)
\(\Rightarrow x-1=\pm30\)
\(\Rightarrow\orbr{\begin{cases}x=31\\x=-29\end{cases}}\)
\(b,\left|12-|4x+1|\right|=5\)
\(\Rightarrow\orbr{\begin{cases}12-\left|4x+1\right|=5\\12-\left|4x+1\right|=-5\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}\left|4x+1\right|=7\\\left|4x+1\right|=17\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}4x+1=7\text{ hoặc}4x+1=-7\\4x+1=17\text{ hoặc}4x+1=-17\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}or\text{ }x=-2\\x=4or\text{ }x=-\frac{9}{2}\end{cases}}\)
x - 1/12 = 75/x - 1
<=> (x - 1).(x - 1) = 12.75
<=> x2 - 2x + 1 = 900
<=> x2 - 2x + 1 - 900 = 0
<=> x2 - 2x + 1 - 899 = 0
<=> (x + 29)(x - 31) = 0
x + 29 = 0 hoặc x - 31 = 0
x = 0 - 29 x = 0 + 31
x = -29 x = 31
=> x = -29 hoặc x = 31