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góc A1 và góc A2 là 2 góc bù nhau => góc A2 = 180*- A1 = 110*
góc A1 và góc A3 là 2 góc đối đỉnh => góc A3 = 70*, góc A2 và góc A4 là 2 góc đối đỉnh => góc A4=110*
Câu 2: góc B1 và góc B2 là 2 góc bù nhau => B1+B2 =180*. Lại có B1-B2 = 60*
=> B1+B2+B1-B2 = 240*
<=> 2B1= 240*
=> B1 = 120*=>B1 =B3=120*(2 góc đối đỉnh)
=> B2 =60*=> B2 =B4 =60*(2 góc đối đỉnh)
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Ta có :
\(\left(\frac{3}{8}-\frac{1}{5}\right)+\left(\frac{5}{8}-x\right)=\frac{1}{5}\)
\(\Rightarrow\frac{3}{8}-\frac{1}{5}+\frac{5}{8}-x=\frac{1}{5}\)
\(\Rightarrow\left(\frac{3}{8}+\frac{5}{8}\right)-\frac{1}{5}-x=\frac{1}{5}\)
\(\Rightarrow1-\frac{1}{5}-x=\frac{1}{5}\)
\(\Rightarrow\frac{4}{5}-x=\frac{1}{5}\)
\(\Rightarrow x=\frac{4}{5}-\frac{1}{5}=\frac{3}{5}\)
| 2x - 1 | + 1 = 4
=> | 2x - 1 | = 3
\(\Rightarrow\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x=4\\2x=-2\end{cases}}\Rightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}\)
8 - | 1 - 3x | = 3
=> | 1 - 3x | = 5
\(\Rightarrow\orbr{\begin{cases}1-3x=5\\1-3x=-5\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}3x=1-5=-4\\3x=1-\left(-5\right)=6\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{-4}{3}\\x=2\end{cases}}\)
\(a)\left(\frac{3}{8}-\frac{1}{5}\right)+\left(\frac{5}{8}-x\right)=\frac{1}{5}.\)
\(\frac{3}{8}-\frac{1}{5}+\frac{5}{8}-x=\frac{1}{5}\)
\(\left(\frac{3}{8}+\frac{5}{8}\right)+\left(-\frac{1}{5}-x\right)=\frac{1}{5}\)
\(1+\left(-\frac{1}{5}-x\right)=\frac{1}{5}\)
\(-\frac{1}{5}-x=\frac{1}{5}-1\)
\(-\frac{1}{5}-x=-\frac{4}{5}\)
\(x=-\frac{1}{5}-\left(-\frac{4}{5}\right)\)
\(x=\frac{3}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
( x - 1 )x+3 = ( x - 1 )x+4
=> ( x - 1 )x+4 - ( x - 1 )x+3 = 0
=> ( x- 1 )x+3 . ( x - 1 - 1 ) = 0
\(\Rightarrow\orbr{\begin{cases}\left(x-1\right)^{x+3}=0\\x-1-1=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\x-2=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) ( x - 1 )3 = 27
=> ( x - 1 )3 = 33
=> x - 1 = 3
=> x = 4
b) x2 + x = 0
=> x . ( x + 1 ) = 0
\(\Rightarrow\orbr{\begin{cases}x=0\\x+1=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=-1\end{cases}}\)
c) ( 2x + 1 )2 = 25
=> ( 2x + 1 )2 = 52 = ( -5 )2
\(\Rightarrow\orbr{\begin{cases}2x+1=5\\2x+1=-5\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x=4\\2x=-6\end{cases}}\Rightarrow\orbr{\begin{cases}x=2\\x=-3\end{cases}}\)
d) ( 2x - 3 )2 = 36
=> ( 2x - 3 )2 = 62 = ( -6 )2
\(\Rightarrow\orbr{\begin{cases}2x-3=6\\2x-3=-6\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x=9\\2x=-3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{9}{2}\\x=\frac{-3}{2}\end{cases}}\)
e) 5x+2 = 625
=> 5x+2 = 54
=> x + 2 = 4
=> x = 2
f) ( x - 1 )x+2 = ( x - 1 )x+4
=> ( x - 1 )x+4 - ( x - 1 )x+2 = 0
=> ( x - 1 )x+2 . [ ( x - 1 )2 - 1 ] = 0
\(\Rightarrow\orbr{\begin{cases}\left(x-1\right)^{x+2}=0\\\left(x-1\right)^2-1=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\\left(x-1\right)^2=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x-1\in\left\{-1;1\right\}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x\in\left\{0;2\right\}\end{cases}}\)
g) ( 2x - 1 )3 = 8
=> ( 2x - 1 )3 = 23
=> 2x - 1 = 2
=> 2x = 3
=> x = \(\frac{3}{2}\)
h) \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.....\frac{31}{64}=2^x\)
\(\Rightarrow\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.....\frac{31}{2.32}=2^x\)
\(\Rightarrow\frac{1.2.3.4.....31}{\left(2.2\right).\left(2.3\right).\left(2.4\right).....\left(2.32\right)}=2^x\)
\(\Rightarrow\frac{2.3.4.....31}{2^{31}.32.\left(2.3.4.....31\right)}=2^x\)
\(\Rightarrow\frac{1}{2^{31}.2^5}=2^x\)\(\Rightarrow\frac{1}{2^{36}}=2^x\)
\(\Rightarrow2^x=2^{-36}\Rightarrow x=-36\)
a)x=4
b)x=0;x=1
c)x=2
d)x=9/2
g)x=-1/2
những cái khác tui lười tính vì nó rắc rối ơn xíu
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(-0,6x-\frac{1}{2}\right)\times\frac{3}{4}-\left(-1\right)=\frac{1}{3}\)
\(\left(-0,6x-\frac{1}{2}\right)\times\frac{3}{4}=\frac{1}{3}+\left(-1\right)\)
\(\left(-0,6x-\frac{1}{2}\right)\times\frac{3}{4}=-\frac{2}{3}\)
\(-0,6x-\frac{1}{2}=-\frac{2}{3}\div\frac{3}{4}\)
\(-0,6x-\frac{1}{2}=-\frac{8}{9}\)
\(-0,6x=-\frac{8}{9}+\frac{1}{2}\)
\(-0,6x=-\frac{7}{18}\)
\(x=-\frac{7}{18}\div\left(-0,6\right)\)
\(x=\frac{35}{54}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{5}{3\times6}+\frac{5}{6\times9}+\frac{5}{9\times12}+....+\frac{5}{99\times102}.\)
Đặt :
\(A=\frac{5}{3\times6}+\frac{5}{6\times9}+\frac{5}{9\times12}+....+\frac{5}{99\times102}.\)
\(\frac{3}{5}\times A=\frac{3}{5}\times\left(\frac{5}{3\times6}+\frac{5}{6\times9}+...+\frac{5}{99\times102}\right)\)
\(\frac{3}{5}A=\frac{3}{3\times6}+\frac{3}{6\times9}+...+\frac{3}{96\times99}\)
\(\frac{3}{5}A=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+....+\frac{1}{96}-\frac{1}{99}\)
\(\frac{3}{5}A=\frac{1}{3}-\frac{1}{99}\)
\(\frac{3}{5}A=\frac{32}{99}\)
\(A=\frac{32}{99}\div\frac{3}{5}=\frac{160}{297}\)
\(A=\frac{5}{3\times6}+\frac{5}{6\times9}+.....+\frac{5}{99\times102}\)
\(A=\frac{5}{3}\left[\left(\frac{1}{3}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{9}\right)+.....+\left(\frac{1}{99}-\frac{1}{102}\right)\right]\)
\(A=\frac{5}{3}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+....+\frac{1}{99}-\frac{1}{102}\right)\)
\(A=\frac{5}{3}\left(\frac{1}{3}-\frac{1}{102}\right)\)
\(A=\frac{5}{3}.\frac{11}{34}\)
\(A=\frac{55}{102}\)