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(x-2)3=216
=>\(\left(x-2\right)^3=6^3\)
=>x-2=6
=>x=8
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{3}+\frac{13}{15}+...+\frac{9997}{9999}\)
\(=1-\frac{2}{3}+1-\frac{2}{15}+...+1-\frac{2}{9999}\)
\(=\left(1+1+...+1\right)-\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\right)\)
\(=50-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(=50-\left(1-\frac{1}{101}\right)\)
Sau bạn tính tiếp là OK rồi
![](https://rs.olm.vn/images/avt/0.png?1311)
47.63 = (55 - 8)(55 + 8)
= 55² - 8²
= 3025 - 64
= 2961
--------
47.(63 - 15) - 63.(47 - 15)
= 47.63 - 47.15 - 63.47 + 63.15
= 47.(63 - 63) + 15.(63 - 47)
= 47.0 + 15.16
= 0 + 240
= 240
47.63 = (55 - 8)(55 + 8)
= 55² - 8²
= 3025 - 64
= 2961
--------
47.(63 - 15) - 63.(47 - 15)
= 47.63 - 47.15 - 63.47 + 63.15
= 47.(63 - 63) + 15.(63 - 47)
= 47.0 + 15.16
= 0 + 240
= 240
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=101-102-103+104-105-106+107-108+109+110
= (101+104+107+109+110)-(102+103+105+106+108)
=701-704
=-3
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Bài 3:
a: \(x=\dfrac{1}{4}-\dfrac{2}{13}=\dfrac{13}{52}-\dfrac{8}{52}=\dfrac{5}{52}\)
b: \(\dfrac{x}{3}=\dfrac{2}{3}-\dfrac{1}{7}\)
nên \(x\cdot\dfrac{1}{3}=\dfrac{14}{21}-\dfrac{3}{21}=\dfrac{11}{21}\)
hay \(x=\dfrac{11}{21}:\dfrac{1}{3}=\dfrac{11}{7}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
S = 1.3 + 2.4 + 3.5 + 4.6 + ..... + 99.101 + 100.102
= 1.(2 + 1) + 2(3 + 1) + 3.(4 + 1) + ......... + 99(100 + 1) + 100.(101 + 1)
= 1.2 + 1 + 2.3 + 1 + 3.4 + 3 + ........ + 99.100 + 99 + 100.101 + 100
= (1.2 + 2.3 + 3.4 + ....... + 100.101 ) + (1 + 2 + 3 + ....... + 100)
Ta có công thức :
1.2+2.3+3.4+....+n(n+1)=n(n+1)(n+2)/3
1+2+3+...+n=n(n+1)/2
Áp dụng vào bài toán ta được :
S=100.101.102/3 +100.101/2
= 343400 + 5050
= 348450
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\Rightarrow\left(2x-15\right)^3\left[\left(2x-15\right)^2-1\right]=0\)
\(\Rightarrow\left(2x-15\right)^3\left(2x-15-1\right)\left(2x-15+1\right)=0\)
\(\Rightarrow\left(2x-15\right)^3\left(2x-16\right)\left(2x-14\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x-15=0\\2x-16=0\\2x-14=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=15\\2x=16\\2x=14\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=8\\x=7\end{matrix}\right.\)
\(63+27.97+18=63+18+27.97=81++27.97=27.3+27.97=27.\left(3+97\right)=27.100=2700\)
2700