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134/43 = 3,1162... bé - lớn : 55/21 ; 134/43 ; 116/37 ; 74/19
55/21 = 2,6190... lớn - bé : (ngược lại)
74/19 = 3,8947...
116/37 = 3,1351...
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a) Ta có : B = 23! + 19! + 15!
= 1.2.3.4..10.11...23 + 1.2.3.4...10.11..19 + 1.2.3.4..10.11..15
= 11(1.2.3...10.12.23 + 1.2.3.4..10.12...19 + 1.2.3.4....10.12...15) \(⋮\)11
b) Lại có B = 23! + 19! + 15!
= 1.2.3.4..10.11...23 + 1.2.3.4...10.11..19 + 1.2.3.4..10.11..15
= 10.11(1.2.3.4..9.12...23 + 1.2.3.4...9.12...19 + 1.2.3.4...9.12...15)
= 110(1.2.3.4..9.12...23 + 1.2.3.4...9.12...19 + 1.2.3.4...9.12...15) \(⋮\)110
BÀI GIẢI:
a) Ta có: B = 23! + 19! + 15!
= 1.2.3. ... .10 .11. ... 23 + 1.2.3. ... .10.11. ... .19 + 1.2.3. ... .10.11. ... .15
= 11 (1.2.3. ... .10.12. ... .23 + 1.2.3. ... .10.12. ... .19 + 1.2.3. ... .10.12. ... .15) \(⋮11\)
b) Ta có: B = 23! + 19! + 15!
= 1.2.3. ... .10 .11. ... 23 + 1.2.3. ... .10.11. ... .19 + 1.2.3. ... .10.11. ... .15
= 10.11 (1.2.3. ... .10.12. ... .23 + 1.2.3. ... .10.12. ... .19 + 1.2.3. ... .10.12. ... .15)
= 110 (1.2.3. ... .10.12. ... .23 + 1.2.3. ... .10.12. ... .19 + 1.2.3. ... .10.12. ... .15) \(⋮110\)
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a: \(=\dfrac{-39+19+10}{12}=\dfrac{-10}{12}=\dfrac{-5}{6}\)
b: \(=\dfrac{2^{30}\cdot3^{16}\cdot7-2^{34}\cdot3^{15}}{2^{28}\cdot3^{21}-2^{28}\cdot3^{17}}\)
\(=\dfrac{2^{30}\cdot3^{15}\left(3\cdot7-2^4\right)}{2^{28}\cdot3^{17}\left(3^4-1\right)}=\dfrac{2^2}{3^2}\cdot\dfrac{21-16}{80}=\dfrac{4}{9}\cdot\dfrac{5}{80}\)
\(=\dfrac{20}{720}=\dfrac{1}{36}\)
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Ta có: \(A=\frac{19^{30}+5}{19^{31}+5}\Rightarrow19A=\frac{19.\left(19^{30}+5\right)}{19^{31}+5}=\frac{19^{31}+95}{19^{31}+5}=\frac{19^{31}+5+90}{19^{31}+5}=1+\frac{90}{19^{31}+5}\)
\(B=\frac{19^{31}+5}{19^{32}+5}\Rightarrow19B=\frac{19.\left(19^{31}+5\right)}{19^{32}+5}=\frac{19^{32}+95}{19^{32}+5}=\frac{19^{32}+5+90}{19^{32}+5}=1+\frac{90}{19^{32}+5}\)
Nên \(19A< 19B\Rightarrow A< B\)
Nhầm: Vì \(\frac{90}{19^{31}+5}>\frac{90}{19^{32}+5}\Rightarrow1+\frac{90}{19^{31}+5}>1+\frac{90}{19^{32}+5}\Rightarrow A>B\)
=-19x100=-1900
=(12.(-19)+(-19).87)-19
=-19(12+87)-19
=-19.99-19
=-1878-19
=-1907