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\(D=\dfrac{2^{10}\cdot3^{31}+2^{40}\cdot3^6}{2^{11}\cdot3^{31}+2^{41}\cdot3^6}\)
\(=\dfrac{2^{10}\cdot3^6\left(3^5+2^{35}\right)}{2^{11}\cdot3^6\left(3^5+2^{35}\right)}=\dfrac{1}{2}\)
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\(A=\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
\(=\dfrac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\)
\(=\dfrac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)
\(=\dfrac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}\)
\(=-\dfrac{2}{6}=-\dfrac{1}{3}\)
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2.3x+2+4.3x+1=10.36
2.3.3x+1+4.3x+1=10.36
6.3x+1+4.3x+1=10.36
10.3x+1=10.36
=>3x+1=36
=>x+1=6 =>x=5
Ai thấy đúng cho mình nha!
\(2.3^{x+2}+4.3^{x+1}=10.3^6\)
\(2.3^{x+2}+2^2.3^{x+1}=2.5.3^6\)
\(2.3^{x+1}\left(3+2\right)=2.5.3^6\)
\(2.3^{x+1}.5=2.5.3^6\)
\(\Rightarrow x+1=6\Rightarrow x=5\)
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\(\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^{10}}\)
\(=\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^{10}}\)
\(=\dfrac{2^{10}\cdot3^8\left(1-3\right)}{2^{10}\cdot3^8\left(1+3^2\right)}=-\dfrac{2}{10}=-\dfrac{1}{5}\)
\(\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^{10}}\)
\(=\dfrac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^{10}}\)
\(=\dfrac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^{10}.3^{10}}\)
\(=\dfrac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8.\left(1+3^2\right)}\)
\(=\dfrac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.10}\)
\(=\dfrac{-2}{10}\)
\(=\dfrac{-1}{5}\)
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a)
\(5A=5+5^2+.....+5^{101}\)
\(\Rightarrow5A-A=\left(5+5^2+.....+5^{101}\right)-\left(1+5+.....+5^{100}\right)\)
\(\Rightarrow4A=5^{101}-1\)
\(\Rightarrow A=\frac{5^{101}-1}{4}\)
b)
\(2B=1+\left(\frac{1}{2}\right)^2+....+\left(\frac{1}{2}\right)^{100}\)
\(\Rightarrow2B-B=\left(1+\frac{1}{2^2}+.....+\frac{1}{2^{100}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+......+\frac{1}{2^{99}}\right)\)
\(\Rightarrow B=1-\frac{1}{2^{100}}\)