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\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+10\right)}{1.10+2.9+3.8+...+10.1}\)
\(=\frac{\left(1+1+...+1\right)+\left(2+2+...+2\right)+...+\left(10\right)}{10.1+8.2+....+1.10}\)
\(=\frac{1.10+2.9+....+10.1}{1.10+2.9+...+10.1}=1\)
\(\frac{1-\frac{2}{10}+x+\frac{1}{5}}{\frac{4}{3}-\frac{2}{3}+\frac{10}{3}}-1=\frac{3}{2}\)
\(\Rightarrow\frac{\frac{4}{5}+x+\frac{1}{5}}{\frac{4-2+10}{3}}=\frac{3}{2}+1\)
\(\Rightarrow\frac{\left(\frac{4}{5}+\frac{1}{5}\right)+x}{4}=\frac{5}{2}\)
\(\Rightarrow1+x=\frac{5}{2}.4\)
\(\Rightarrow1+x=10\)
\(\Rightarrow x=10-1\)
\(\Rightarrow x=9\)
Vậy x = 9
_Chúc bạn học tốt_
(1-2/10+x+1/5)/(4/3-2/3+10/3)=3/2+1
(1-2/10+x+1/5)/(4/3-2/3+10/3)=5/2
=>1-2/10+x+1/5=5
=>8/10+x=5-1/5
=>4/5+x=24/5
=>x=24/5-4/5
=>x=4
Câu 1 : \(\frac{10}{3}\cdot x-\frac{1}{2}=\frac{1}{10}\)
\(\Rightarrow\frac{10}{3}\cdot x=\frac{3}{5}\Rightarrow x=\frac{9}{50}\)
Câu 2 : \(\frac{1}{3}\cdot x+\frac{1}{3}\cdot x=\frac{1}{8}\Rightarrow x\cdot\left(\frac{1}{3}+\frac{1}{3}\right)=\frac{1}{8}\)
\(x\cdot\frac{2}{3}=\frac{1}{8}\Rightarrow x=\frac{3}{16}\)
Câu 3 : \(\left[3x-1\right]\left[\frac{1}{2}x-\frac{2}{5}\right]=0\)
\(\Rightarrow3x-1=0\)hoặc \(\frac{1}{2}x-\frac{2}{5}=0\)
( vô lí ) x = 4/5
Ta có: 1/2*2 < 1/1*2 = 1 - 1/2
1/3*3 < 1/2*3 = 1/2 -1/3
1/4*4 < 1/3*4 = 1/3 - 1/4
..................................
1/10*10 < 1/9*10 = 1/9 - 1/10
=> 1/2*2 + 1/3*3 + 1/4*4 + ... + 1/10*10 < 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10 = 1 - 1/10 = 9/10 < 1.
=> 1/2*2 + 1/3*3 + 1/4*4 + ... + 1/10*10 < 1.
\(\dfrac{2}{3}+\dfrac{1}{2}-\dfrac{1}{10}\\ =\dfrac{7}{6}-\dfrac{1}{10}\\ =\dfrac{64}{60}\)