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Mấy bài kia mình giải cho bạn rùi bây giờ mk giải bài 4 nhá
Gọi số nguyên cần tìm là \(a\) theo đề bài ta có :
\(\frac{151-a}{161-a}=\frac{21}{26}\)
\(\Rightarrow\)\(21\left(161-a\right)=26\left(151-a\right)\)
\(\Rightarrow\)\(3381-21a=3926-26a\)
\(\Rightarrow\)\(-21a+26a=3926-3381\)
\(\Rightarrow\)\(5a=545\)
\(\Rightarrow\)\(a=\frac{545}{5}\)
\(\Rightarrow\)\(a=109\)
Vậy số nguyên cần tìm là \(109\)
Chúc bạn học tốt ~
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Ta có :
\(B=\frac{2004+2005}{2005+2006}=\frac{2004}{2005+2006}+\frac{2005}{2005+2006}< \frac{2004}{2005}+\frac{2005}{2006}=A\)
\(\Rightarrow\)\(B< A\) hay \(A>B\)
Vây \(A>B\)
Chúc bạn học tốt ~
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a, \(\frac{-11}{12}>\frac{17}{-18}\)
b\(\frac{2}{5}< \frac{5}{7}\)
c\(\frac{-3}{4}>\frac{-6}{7}\)
d\(\frac{19}{18}>\frac{2005}{2004}\)
e\(\frac{72}{73}< \frac{98}{99}\)
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Bài 1:19.C=\(\frac{19^{209}+19}{19^{209}+1}\)=\(\frac{19^{209}+1+18}{19^{209}+1}\)=\(\frac{19^{209}+1}{19^{209}+1}\)+\(\frac{18}{19^{209}+1}\)=1+\(\frac{18}{19^{209}+1}\)19D=\(\frac{19^{210}+19}{19^{210}+1}\)=\(\frac{19^{210}+1+18}{19^{210}+1}\)=\(\frac{19^{210}+1}{19^{210}+1}\)+\(\frac{18}{19^{210}+1}\)=1+\(\frac{18}{19^{210}+1}\).Vì \(\frac{18}{19^{209}+1}\)>\(\frac{18}{19^{210}+1}\)nên 19A>19B\(\Rightarrow\)A>B
19D=\(\frac{\left(19^{209}+1\right).19}{19^{210}+1}=\frac{19^{210}+19}{19^{210}+1}=\frac{\left(19^{210}+1\right)+18}{19^{210}+1}=\frac{19^{210}+1}{19^{210}+1}+\frac{18}{19^{210}+1}=1+\frac{18}{19^{210}+1}\)
Vì 19C>19D nên C>D
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Vì \(\frac{2005^{2005}+1}{2005^{2006}+1}\) < 1
Nên \(\frac{2005^{2005}+1}{2005^{2006}+1}\) < \(\frac{2005^{2005}+1+2004}{2005^{2006}+1+2004}\)
Ta có: \(\frac{2005^{2005}+1+2004}{2005^{2006}+1+2004}=\frac{2005^{2005}+2005}{2005^{2006}+2005}=\frac{2005\left(2005^{2004}+1\right)}{2005\left(2005^{2005}+1\right)}=\frac{2005^{2004}+1}{2005^{2005}+1}\)
Nên: \(\frac{2005^{2005}+1}{2005^{2006}+1}\) < \(\frac{2005^{2004}+1}{2005^{2005}+1}\)
=> A < B
Ta có :
19/18 = 19/19 - 18/19 = 1/19
2005/2004 = 2005/2005 - 2004/2005 = 1/2005
Ta thấy 1/19 > 1/2005 Vậy 19/18 < 2005/2004
19/18 >2005/2004