tìm x biết
1)\(-\frac{2}{3}\cdot\left(x-\frac{1}{4}\right)=\frac{1}{3}\cdot\left(2x-1\right)\)
2)\(\frac{1}{5}\cdot2^x+\frac{1}{5}\cdot2^{x+1}=\frac{1}{5}\cdot2^7+\frac{1}{3}\cdot2^8\)
Những câu hỏi liên quan
1 ) Tìm x biết
a) \(x^{10}\cdot\left(x^2\right)^{10}\cdot\left(x^3\right)^{10}\cdot...\cdot\left(x^{10}\right)^{10}\)
b)\(\frac{1}{2}\cdot2^x+4\cdot2^x=9\cdot2^5\)
c)\(3\cdot2^{x+2}=5\cdot2^3\)
tìm x1, frac{1}{3}x+frac{2}{5}left(x-1right)02, frac{1}{3}+frac{1}{6}+frac{1}{10}+...+frac{2}{xleft(x+1right)}frac{49}{50}3, x-left(frac{11}{12}-xright)x-frac{3}{4}4, -29-4cdot|3x+6|-415, frac{1}{5}cdot2x+frac{1}{3}cdot2^{x+1}frac{1}{5}cdot2^7+frac{1}{3}cdot2^8 MỌI NGƯỜI LÀM ĐƯỢC CÂU NÀO THÌ LÀM GIÚP EM Ạ
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tìm x
1, \(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)
2, \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
3, \(x-\left(\frac{11}{12}-x\right)=x-\frac{3}{4}\)
4, \(-29-4\cdot|3x+6|=-41\)
5, \(\frac{1}{5}\cdot2x+\frac{1}{3}\cdot2^{x+1}=\frac{1}{5}\cdot2^7+\frac{1}{3}\cdot2^8\)
MỌI NGƯỜI LÀM ĐƯỢC CÂU NÀO THÌ LÀM GIÚP EM Ạ
\(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x=0+\frac{2}{5}\)
\(\Leftrightarrow x\left(\frac{1}{3}+\frac{2}{5}\right)=\frac{2}{5}\)
\(\Leftrightarrow x\left(\frac{5}{15}+\frac{6}{15}\right)=\frac{2}{5}\)
\(\Leftrightarrow\frac{11}{15}x=\frac{2}{5}\)
\(\Leftrightarrow x=\frac{2}{5}\div\frac{11}{15}\)
\(\Leftrightarrow x=\frac{6}{11}\)
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\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{49}{50}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\div2\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\times\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{50}{100}-\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{100}\)
\(\Leftrightarrow x+1=100\)
\(\Leftrightarrow x=100-1\)
\(\Leftrightarrow x=99\)
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\(x-\left(\frac{11}{12}+x\right)=x-\frac{3}{4}\)
\(\Leftrightarrow x-\frac{11}{12}-x=x-\frac{3}{4}\)
\(\Leftrightarrow-\frac{11}{12}=x-\frac{3}{4}\)
\(\Leftrightarrow x=\frac{-11}{12}+\frac{3}{4}\)
\(\Leftrightarrow x=\frac{-11}{12}+\frac{9}{12}\)
\(\Leftrightarrow x=\frac{-2}{12}=\frac{-1}{6}\)
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Xem thêm câu trả lời
A=\(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)........\left(1-\frac{1}{2004}\right)\)
\(B=5\frac{9}{10}:\frac{3}{2}-\left(2\frac{1}{3}\cdot4\frac{1}{2}-2\cdot2\frac{1}{3}\right):\frac{7}{4}\)
A = \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{2004}\right)\)
A = \(\left(\frac{2}{2}-\frac{1}{2}\right).\left(\frac{3}{3}-\frac{1}{3}\right).\left(\frac{4}{4}-\frac{1}{4}\right)....\left(\frac{2004}{2004}-\frac{1}{2004}\right)\)
A = \(\frac{1}{2}\)x\(\frac{2}{3}.\)\(\frac{3}{4}....\)\(\frac{2003}{2004}\)
A = \(\frac{1}{2004}\)
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\(\frac{\left(-3\right)-\frac{1}{2}\cdot\left(7\frac{1}{2}-5,3\right)\cdot2-3x}{-6,2+2\cdot\left(\frac{1}{2}+1,6\right)}=10,9+x\)
b3 tính nhanh nếu có thểa frac{1}{2}+frac{1}{4}+frac{1}{8}+frac{1}{16}+frac{1}{32}b frac{1}{2}cdotfrac{1}{2}+frac{1}{2}cdotfrac{1}{3}+frac{1}{3}cdotfrac{1}{4}+frac{1}{4}cdotfrac{1}{5}+frac{1}{5}cdotfrac{1}{6}c1frac{1}{24}cdot5frac{2}{5}cdot2-3frac{7}{9}cdot2frac{2}{17}d2frac{3}{13}cdotfrac{26}{58}cdot4cdot2frac{15}{24}cdotfrac{8}{21}e left(1-frac{6}{11}right)-frac{5}{11}fleft(frac{15}{7}-frac{2}{3}right)+frac{2}{3}gleft(frac{5}{8}-frac{1}{4}right)+frac{3}{8}hfrac{3}{3cdot5}+frac{3}{5cdot8}+frac{...
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b3 tính nhanh nếu có thể
a \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
b \(\frac{1}{2}\cdot\frac{1}{2}+\frac{1}{2}\cdot\frac{1}{3}+\frac{1}{3}\cdot\frac{1}{4}+\frac{1}{4}\cdot\frac{1}{5}+\frac{1}{5}\cdot\frac{1}{6}\)
c\(1\frac{1}{24}\cdot5\frac{2}{5}\cdot2-3\frac{7}{9}\cdot2\frac{2}{17}\)
d\(2\frac{3}{13}\cdot\frac{26}{58}\cdot4\cdot2\frac{15}{24}\cdot\frac{8}{21}\)
e \(\left(1-\frac{6}{11}\right)-\frac{5}{11}\)
f\(\left(\frac{15}{7}-\frac{2}{3}\right)+\frac{2}{3}\)
g\(\left(\frac{5}{8}-\frac{1}{4}\right)+\frac{3}{8}\)
\(h\frac{3}{3\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+\frac{3}{14\cdot17}+\frac{3}{17\cdot20}\)
a) \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}\)
\(=1-\frac{1}{32}=\frac{31}{32}\)
b) \(\frac{1}{2}.\frac{1}{2}+\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}\)\
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\frac{1}{4}-\frac{1}{6}=\frac{1}{12}\)
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1. Tính:
a)\(81^3:3^5\)
b)\(16\cdot2^4\cdot\frac{1}{32}\cdot2^3\)
2. Tìm x:
a) \(\left(x-1\right)^5=32\)
b) \(\left(2^3:4\right)\cdot2^{\left(x+1\right)}=64\)
\(3^2\cdot\frac{1}{243}\cdot81^2\cdot\frac{1}{3^3}\)
\(\left(4\cdot2^5\right):\left(2^3\cdot\frac{1}{6}\right)\)
\(3^2\times\frac{1}{243}\times81^2\times\frac{1}{3^3}\)
\(=3^2\times\frac{1}{3^5}\times\left(3^4\right)^2\times\frac{1}{3^3}\)
\(=\left(3^2\times3^8\right)\times\left(\frac{1}{3^5}\times\frac{1}{3^3}\right)\)
\(=3^{10}\times\frac{1}{3^8}\)
\(=3^2\)
\(=9\)
\(\left(4\times2^5\right)\div\left(2^3\times\frac{1}{6}\right)\)
\(=\left(2^2\times2^5\right)\div\left(2^3\times\frac{1}{2\times3}\right)\)
\(=2^7\div2^2\times3\)
\(=2^5\times3\)
\(=96\)
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\(3^2.\frac{1}{243}.81^2.\frac{1}{3^3}\)
\(=3^2.\frac{1}{3^5}.\left(3^4\right)^2.\frac{1}{3^3}\)
\(=\left(3^2.3^8\right).\left(\frac{1}{3^5}.\frac{1}{3^3}\right)\)
\(=3^{10}.3^{-8}\)
\(=3^2=9\)
\(\left(4.2^5\right):\left(2^3.\frac{1}{6}\right)\)
\(=2^7:2^2.3\)
\(=2^5.3\)
\(=96\)
Bài 1:
a) \(\frac{1}{1}\cdot2+\frac{1}{2}\cdot3+\frac{1}{3}\cdot4+...+\frac{1}{n}\cdot\left(n+1\right)\)
b) \(\frac{1}{1}\cdot2\cdot3+\frac{1}{2}\cdot3\cdot4+\frac{1}{3}\cdot4\cdot5+...+\frac{1}{a}\cdot\left(a+1\right)\cdot\left(a+2\right)\)
tập hợp các số nguyên x thỏa mãn
\(x\cdot\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\right)<1\frac{6}{7}\)
Lời giải:
$x(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7})< 1\frac{6}{7}$
$x(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7})< \frac{13}{7}$
$x(1-\frac{1}{7})< \frac{13}{7}$
$x.\frac{6}{7}< \frac{13}{7}$
$x< \frac{13}{7}: \frac{6}{7}=\frac{13}{6}$
Vì $x$ là số nguyên nên $x\leq 2$
Vậy $x$ là các số nguyên sao cho $x\leq 2$.
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