A = 2 * 69 - 45 * 94 / 210 * 38 + 68 * 20
A= 2 * 84 * 272 + 4 * 69 / 27 * 67 + 27 * 40 * 94
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a: \(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
=>\(2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)
=>\(2A+A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2+2^{100}-2^{99}+...+2^2-2\)
=>\(3A=2^{101}-2\)
=>\(A=\dfrac{2^{101}-2}{3}\)
b: Sửa đề: \(A=\dfrac{2\cdot8^4\cdot27^2+4\cdot6^9}{2^7\cdot6^7+2^7\cdot40\cdot9^4}\)
\(A=\dfrac{2\cdot2^{12}\cdot3^6+2^2\cdot2^9\cdot3^9}{2^7\cdot2^7\cdot3^7+2^7\cdot2^3\cdot5\cdot3^8}\)
\(=\dfrac{2^{11}\cdot3^6\left(2^3+3^3\right)}{2^{10}\cdot3^7\left(2^4+5\cdot3\right)}\)
\(=\dfrac{2}{3}\cdot\dfrac{4+27}{16+15}=\dfrac{2}{3}\)
c: \(B=\dfrac{4^5\cdot9^4-2\cdot6^4}{2^{10}\cdot3^8+6^8\cdot20}\)
\(=\dfrac{2^{10}\cdot3^8-2\cdot2^4\cdot3^4}{2^{10}\cdot3^8+2^8\cdot2^2\cdot5\cdot3^8}\)
\(=\dfrac{2^5\cdot3^4\left(2^5\cdot3^4-1\right)}{2^{10}\cdot3^8\left(1+5\right)}=\dfrac{1}{2^5\cdot3^4}\cdot\dfrac{32\cdot81-1}{6}\)
\(=\dfrac{2591}{2^6\cdot3^5}\)
b: \(\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)
\(=\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+3^8\cdot2^{10}\cdot5}\)
\(=\dfrac{2^{10}\cdot3^8\left(1-3\right)}{2^{11}\cdot3^9}\)
\(=\dfrac{1}{2}\cdot\dfrac{-2}{3}=\dfrac{-1}{3}\)
Biểu thức =\(\frac{15}{34}+\frac{4}{27}+\frac{19}{34}+\frac{23}{27}\) ( rút gọn đó )
=\(\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{4}{27}+\frac{23}{27}\right)\)
=\(\frac{15+19}{34}+\frac{4+23}{27}\)= \(\frac{34}{34}+\frac{27}{27}\)
= \(1+1=2\)
Oke nhá !!
\(\frac{15}{34}+\frac{4}{27}+\frac{38}{68}+\frac{69}{81}=\frac{15}{34}+\frac{4}{27}+\frac{19}{34}+\frac{23}{27}\)
\(=\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{4}{27}+\frac{23}{27}\right)\)
\(=\frac{34}{34}+\frac{27}{27}=1+1=2\)
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