\(x=4095\)

\(x=5460\)

a) \(\dfrac{7}{13}\)\(\times\)\(\dfrac{7}{15}\)-\(\dfrac{5}{12}\)\(\times\)\(\dfrac{21}{39}+\dfrac{49}{91}\)\(\times\)\(\dfrac{8}{15}\)

= \(\dfrac{7}{13}\)\(\times\)\(\dfrac{7}{15}\)-\(\dfrac{5}{12}\times\dfrac{7}{13}+\dfrac{7}{13}\times\dfrac{8}{15}\)

= \(\dfrac{7}{13}\left(\dfrac{7}{15}-\dfrac{5}{12}+\dfrac{8}{15}\right)\)

= \(\dfrac{7}{13}\times\dfrac{7}{12}\)

= \(\dfrac{49}{156}\)

b) \(\left(\dfrac{12}{199}+\dfrac{23}{200}-\dfrac{34}{201}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\)

= \(\left(\dfrac{12}{199}+\dfrac{23}{200}-\dfrac{34}{201}\right)\times0\)

= 0

\(5\left|x\right|=7-\left(-8\right)\)

<=> 5|x|=15

<=> |x|=3

<=> \(\orbr{\begin{cases}x=3\\x=-3\end{cases}}\)

*) -2|x-3|=-10

<=> |x-3|=5

<=> \(\orbr{\begin{cases}x-3=5\\x-3=-5\end{cases}\Leftrightarrow\orbr{\begin{cases}x=8\\x=-2\end{cases}}}\)

*) |x-9|=|-91|

<=> |x-9|=91

<=> \(\orbr{\begin{cases}x-9=91\\x-9=-91\end{cases}\Leftrightarrow\orbr{\begin{cases}x=100\\x=-82\end{cases}}}\)

5|x|=7-(-8)

5|x|=7+8

5|x|=15

  |x|=15:5

  |x|=3

=> x=+3

vậy x=+3

-2|x-3|=-10

   |x-3|=-10:(-2)

   |x-3|=5

\(\Rightarrow\orbr{\begin{cases}x-3=5\\x-3=-5\end{cases}\Rightarrow\orbr{\begin{cases}x=8\\x=-2.\end{cases}}}\)

Vậy x=8 hoặc x=-2

|x-9|=|-91|

|x-9|=91

\(\Rightarrow\orbr{\begin{cases}x-9=91\\x-9=-91\end{cases}}\Rightarrow\orbr{\begin{cases}x=100\\x=-82\end{cases}}\)

Vậy x=100 hoặc x=-82

\(\frac{x}{15}=\frac{3}{5}+\frac{-2}{3}\)

\(\frac{x}{15}=\frac{-1}{15}\)

=> \(x=-1\)

\(\frac{x}{182}=\frac{-6}{14}\cdot\frac{35}{91}\)

\(\frac{x}{182}=\frac{-15}{91}\)

=> \(91x=182\cdot\left(-15\right)\)

=> \(91x=-2730\)

=> \(x=-30\)

g, \(\frac{x}{15}=\frac{3}{5}+\frac{-2}{3}\Leftrightarrow\frac{x}{15}=\frac{3}{5}-\frac{2}{3}\Leftrightarrow\frac{x}{15}=-\frac{1}{15}\)

\(\Leftrightarrow x=-1\)

h, \(\frac{x}{182}=\frac{-6}{14}.\frac{35}{91}\Leftrightarrow\frac{x}{182}=-\frac{15}{91}\Leftrightarrow\frac{x}{182}=\frac{-30}{182}\)

\(\Leftrightarrow x=-30\)

P/s: Bài này chỉ tính được giá trị "gần đúng" của biểu thức thôi nhé!

\(\frac{21}{54}+\frac{3}{75}:\frac{\left(\frac{39}{65}+0,415-\frac{33}{600}\right)\frac{21}{91}}{7^2-18,25+13\frac{15}{36}-16\frac{17}{102}}\)

\(\Leftrightarrow\frac{21}{54}+\frac{3}{75}:\frac{\left(0,6+0,415-0,055\right)0,23}{49-18,25+\frac{483}{36}-\frac{1649}{102}}\)

\(\Leftrightarrow\frac{21}{54}+\frac{3}{75}:\frac{\left(0,6+0,415-0,055\right)0,23}{49-18,25+13,41-16,1}\)

\(\Leftrightarrow\frac{21}{54}+\frac{3}{75}:\frac{0,96.0,23}{28,06}\Leftrightarrow\frac{21}{54}+\frac{3}{75}:\frac{0,2208}{28,06}\)

\(\Leftrightarrow\frac{21}{54}+\left(\frac{3}{75}:\frac{0,2208}{28,06}\right)\Leftrightarrow\frac{21}{54}+\left(\frac{3}{75}.\frac{28,06}{0,2208}\right)=\frac{21}{54}+\frac{61}{12}=\frac{197}{36}\)

P/s: Giải bài này mà mệt cả đầu =((

Bài 1 :

a, \(2^x+2^{x+1}=24\)

\(\Rightarrow2^x.1+2^x.2=24\)

\(\Rightarrow2^x\left(1+2\right)=24\)

\(\Rightarrow2^x=24\div3\)

\(\Rightarrow2^x=8=2^3\)

Vậy : x = 3

b, \(x^2-x=0\)

\(\Rightarrow x.x-x.1=0\)

\(\Rightarrow x\left(x-1\right)=0\)

Để : \(x\left(x-1\right)=0\Rightarrow x-1=0\)

\(\Rightarrow x=1\)

Vậy x = 1

Bài 2 :

a, \(Q=3+3^3+3^5+...+3^{101}\)

\(\Rightarrow9Q=3^3+3^5+3^7+...+3^{103}\)

\(\Rightarrow9Q-Q=\left(3^3+3^5+3^7+...+3^{103}\right)-\left(3+3^3+3^5+...+3^{101}\right)\)

\(\Rightarrow8Q=3^{103}-3\)

\(\Rightarrow Q=\frac{3^{103}-3}{8}\)

b, \(Q=3+3^3+3^5+...+3^{101}\)

\(\Rightarrow Q=\left(3+3^3+3^5\right)+\left(3^7+3^9+3^{11}\right)+...+\left(3^{97}+3^{99}+3^{101}\right)\)

\(\Rightarrow Q=\left(3+3^3+3^5\right)+3^6\left(3+3^3+3^5\right)+...+3^{96}\left(3+3^3+3^5\right)\)

\(\Rightarrow Q=1.273+3^6.273+...+3^{96}.273\)

\(\Rightarrow Q=\left(1+3^6+...+3^{96}\right)273\)

Vì : \(1+3^6+...+3^{96}\in N\) ; \(273=3.91\Rightarrow Q⋮91\)

Vậy ...

Phương An

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