1. So sánh
\(\dfrac{-7}{12}< \dfrac{x}{46}\overline{< }\dfrac{8}{-15}\)
Nhanh lên mình cần gấp
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a: =6x5/4=30/4=15/2
b: =8x7/12=56/12=14/3
c: =5x8/7=40/7
d: =15x3/5=9
a: =6x5/4=30/4=15/2
b: =8x7/12=56/12=14/3
c: =5x8/7=40/7
d: =15x3/5=9
Ta có \(\dfrac{1}{2^2}< \dfrac{1}{1.2};\dfrac{1}{3^2}< \dfrac{1}{2.3};...;\dfrac{1}{20^2}< \dfrac{1}{19.20}\)
Cộng vế với vế ta được
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{20^2}< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{19}-\dfrac{1}{20}\)
\(\Rightarrow T< 2-\dfrac{1}{20}=\dfrac{39}{20}\)
mà 39/20 < 8/7 => T < 8/7
\(x=\dfrac{5}{8}+\dfrac{1}{8}\)
\(x=\dfrac{6}{8}=\dfrac{3}{4}\)
\(a,\\ =>n-3\inƯ\left(-7\right)\\ Ư\left(-7\right)=\left\{1;-1;7;-7\right\}\\ =>\left\{{}\begin{matrix}n-3=1\\n-3=-1\\n-3=7\\n-3=-7\end{matrix}\right.\\ =>\left\{{}\begin{matrix}n=4\\n=2\\n=10\\n=-4\end{matrix}\right.\)
\(b,\dfrac{n-5}{n+1}=1-\dfrac{6}{n+1}\\ =>n+1\inƯ\left(6\right)\\ Ư\left(6\right)=\left\{1;-1;2;-2;3;-3;6;-6\right\}\\ =>\left\{{}\begin{matrix}\left\{{}\begin{matrix}n+1=1\\n+1=-1\\n+1=2\\n+1=-2\end{matrix}\right.\\\left\{{}\begin{matrix}n+1=3\\n+1=-3\\n+1=6\\n+1=-6\end{matrix}\right.\end{matrix}\right.=>\left\{{}\begin{matrix}\left\{{}\begin{matrix}n=0\\n=-2\\n=1\\n=-3\end{matrix}\right.\\\left\{{}\begin{matrix}n=2\\n=-4\\n=5\\n=-7\end{matrix}\right.\end{matrix}\right.\)
\(\dfrac{-7}{12}\) < \(\dfrac{x}{46}\) < \(\dfrac{-8}{-15}\)
\(\dfrac{-7}{12}\) < \(\dfrac{x}{46}\) < \(\dfrac{8}{15}\)
12 = 22.3; 46 = 2.23; 15 = 3.5 => MCNN = 22.3.23.5 = 1380
\(\dfrac{-805}{1380}\) < \(\dfrac{30x}{1380}\) < \(\dfrac{736}{1380}\)
-805 < 30\(x\) < 736
\(-\dfrac{805}{30}\) < \(x\) < \(\dfrac{736}{30}\)
\(\dfrac{-161}{6}\) < \(x\)< \(\dfrac{368}{15}\)
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