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\(x:\left(9+\frac{1}{2}-\frac{3}{2}\right)=\frac{2\left(\frac{1}{5}+\frac{1}{9}+\frac{1}{11}\right)}{8\left(\frac{1}{5}+\frac{1}{9}+\frac{1}{11}\right)}\)
\(x:8=\frac{1}{4}\)
x=2
a. \(\frac{x+1}{2}=\frac{8}{x+1}\)
\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=8.2\)
\(\Leftrightarrow\left(x+1\right)^2=16\)
\(\Leftrightarrow\left(x+1\right)^2=2^4\)
\(\Leftrightarrow\left(x+1\right)=2^2\)
\(\Leftrightarrow\left(x+1\right)=4\)
\(\Leftrightarrow x=4-1=3\)
b. \(x:\left(9\frac{1}{2}-\frac{3}{2}\right)=\frac{0,4+\frac{2}{9}-\frac{2}{11}}{1,6+\frac{8}{9}-\frac{8}{11}}\)
\(\Leftrightarrow x:\left(\frac{10}{2}-\frac{3}{2}\right)=\frac{0,4+0,2-0,18}{1,6+0,8-0,72}\)
\(\Leftrightarrow x:\frac{7}{2}=\frac{\frac{21}{50}}{\frac{42}{25}}\)
\(\Leftrightarrow x=\frac{\frac{21}{50}}{\frac{42}{25}}.\frac{7}{2}\Leftrightarrow x=\frac{1}{4}.\frac{7}{2}=\frac{7}{8}\)
a ) \(\frac{x+1}{2}=\frac{8}{x+1}\)
\(\Rightarrow\left(x+1\right).\left(x+1\right)=2.8\)
\(\Rightarrow\left(x+1\right)^2=16\)
\(\Rightarrow\orbr{\begin{cases}x+1=4\\x+1=-4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=4-1\\x=-4-1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=3\\x=-5\end{cases}}\)
Dấu " \(\orbr{\begin{cases}\\\end{cases}}\)là hoặc nha !!!
Bài 1 :
S = \(\frac{6}{2.5}+\frac{6}{5.8}+...+\frac{6}{29.32}\)
= 2 . \(\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{29.32}\right)\)
= 2 . \(\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{29}-\frac{1}{32}\right)\)
= 2 . \(\left(\frac{1}{2}-\frac{1}{32}\right)\)= ....
Bài 1:
a) Ta có: \(\frac{2^8\cdot4\cdot13+2^7\cdot8\cdot65}{2^9\cdot39}\)
\(=\frac{2^8\cdot4\cdot13+2^8\cdot4\cdot13\cdot5}{2^9\cdot39}\)
\(=\frac{2^{10}\cdot13\left(1+5\right)}{2^9\cdot13\cdot3}=\frac{6}{3}=2\)
b) Đặt \(A=4+2^2+2^3+2^4+...+2^{20}\)
Ta có: \(A=4+2^2+2^3+2^4+...+2^{20}\)
\(\Rightarrow2A=2^3+2^3+2^4+...+2^{21}\)
Ta có: \(2A-A=2^3+2^{21}-2^2-2^2=8+2^{21}-8=2^{21}\)
hay \(A=2^{21}\)
Vậy: \(4+2^2+2^3+2^4+...+2^{20}=2^{21}\)
`Answer:`
Vì đề bài khá khó nhìn nên mình làm thành hai bài nhé. Đề nào đúng thì bạn tham khảo.
`x : (9 1/2 - 3/2 ) = 0,4 + 2/9 - 2/11 . 1/6 + 8/9 - 8/11`
`=> x : ( 19/2 - 3/2 ) = 28/45 - 1/33 + 8/9 - 8/11`
`=> x : 8 = 293/495 + 8/9 - 8/11`
`=> x : 8 = 733/495 - 8/11`
`=> x : 8 = 373/495`
`=> x = 373/495 .8`
`=> x = 2984/495`
`x : ( 9 1/2 - 3/2 ) = (0,4 + 2/9 - 2/11 )/(1,6 + 8/9 - 8/11 )`
`=> x : (19/2 - 3/2 ) = (2 . (1/5 + 1/9 - 1/11))/(8.(1/5 + 1/9 - 1/11))`
`=> x : 8 = 2/8`
`=> x = 2/8 .8`
`=> x = 2`