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=>x - 3 0 = 6001 hoặc x - 30 = -6001
=> x = 6031 hoặc x = -5971
BÀi nay không khó lắm
Dễ thấy vế bên phải bằng 0 vì \(\frac{3^6}{9}-81=0\)
=> lx - 30 l - 6001 = 0
=> lx - 30 l = 6001
Tự làm tiếp
\(\frac{8}{81}\left(\frac{-5}{16}-\frac{3}{8}x\right)=\frac{9}{64}\)
\(\frac{-5}{16}-\frac{3}{8}x=\frac{9}{64}.\frac{81}{9}=\frac{81}{64}\)
\(-\frac{3}{8}x=\frac{-5}{16}-\frac{81}{64}=\frac{-20}{64}-\frac{81}{64}=\frac{-101}{64}\)
\(x=\frac{-101}{64}.\frac{-8}{3}=\frac{101}{3}\)
1.
\(\frac{2x+3}{4}-\frac{5x+3}{6}=\frac{3-4x}{12}\)
\(MC:12\)
Quy đồng :
\(\Rightarrow\frac{3.\left(2x+3\right)}{12}-\left(\frac{2.\left(5x+3\right)}{12}\right)=\frac{3x-4}{12}\)
\(\frac{6x+9}{12}-\left(\frac{10x+6}{12}\right)=\frac{3x-4}{12}\)
\(\Leftrightarrow6x+9-\left(10x+6\right)=3x-4\)
\(\Leftrightarrow6x+9-3x=-4-9+16\)
\(\Leftrightarrow-7x=3\)
\(\Leftrightarrow x=\frac{-3}{7}\)
2.\(\frac{3.\left(2x+1\right)}{4}-1=\frac{15x-1}{10}\)
\(MC:20\)
Quy đồng :
\(\frac{15.\left(2x+1\right)}{20}-\frac{20}{20}=\frac{2.\left(15x-1\right)}{20}\)
\(\Leftrightarrow15\left(2x+1\right)-20=2\left(15x-1\right)\)
\(\Leftrightarrow30x+15-20=15x-2\)
\(\Leftrightarrow15x=3\)
\(\Leftrightarrow x=\frac{3}{15}=\frac{1}{5}\)
Dễ thấy (\(\frac{3}{4}\)-81); (\(\frac{3^2}{5}\)-81); (\(\frac{3^3}{6}\)-81);... (\(\frac{3^{2007}}{2010}\)-81) có dạng (\(\frac{3^x}{3+x}\)-81) và x\(\varepsilon\){1;2;3;...2007}.
Nếu x=6 thì \(\frac{3^x}{3+x}\)-81=\(\frac{3^6}{3+6}\)-81=0
=> (\(\frac{3}{4}\)-81) (\(\frac{3}{4}\)-81)(\(\frac{3^3}{6}\)-81)...(\(\frac{3^6}{3+6}\)-81)...(\(\frac{3^{2007}}{2010}\)-81)=0
Mà |x-30|-6001=(\(\frac{3}{4}\)-81) (\(\frac{3}{4}\)-81)(\(\frac{3^3}{6}\)-81)...(\(\frac{3^6}{3+6}\)-81)...(\(\frac{3^{2007}}{2010}\)-81)
=>|x-30|-6001=0
=>|x-30|=6001
=>x-30=6001 hoặc x-30=-6001
=>x=6031 hoặc x=-5971
-------------------The end----------------
\(\text{|x - 30| - 6001 = }\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...\left(\frac{3^{2007}}{2010}-81\right)\)
\(\Rightarrow\text{ |x - 30| - 6001 = }\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...\left(\frac{3^6}{9}-3^4\right)...\left(\frac{3^{2007}}{2010}-81\right)\)
\(\Rightarrow\left|x-30\right|- 6001 = \left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...\left(3^4-3^4\right)...\left(\frac{3^{2007}}{2010}-81\right)\)
\(\Rightarrow|x - 30| - 6001 = \left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...0...\left(\frac{3^{2007}}{2010}-81\right)\)
\(\Rightarrow\text{|x - 30| - 6001 = }0\)
\(\Rightarrow\left|x-30\right|=6001\)
\(\Rightarrow x-30=6001\)hoặc \(x-30=-6001\)
\(\Rightarrow x=6031\)hoặc\(x=-5971\)
Vậy: x= 6031 hoặc x= -5971
(Nói thật thì mình mới lớp 7, đây có phải của lớp 8 không?)