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a)
\(\frac{64}{85}< \frac{64}{81}< \frac{73}{81}\)
=>\(\frac{64}{85}< \frac{73}{81}\)
b)
\(\frac{25}{26}=\frac{25.1010}{26.1010}=\frac{25250}{26260}\)
Ta có: \(1-\frac{25250}{26260}=\frac{1010}{26260}\)
\(1-\frac{25251}{26261}=\frac{1010}{26261}\)
Vì \(\frac{1010}{26260}>\frac{1010}{26261}\) nên \(\frac{25}{26}< \frac{25251}{26261}\)
a)\(\frac{64}{85}\)<\(\frac{64}{81}\)<\(\frac{73}{81}\)
b)\(\frac{25}{26}\)=\(\frac{25250}{26260}\)=\(1\)- \(\frac{1010}{26260}\)< \(1\)- \(\frac{1010}{26261}\)= \(\frac{25251}{26261}\)
Ta có:
\(\frac{25}{26}=\frac{2525}{2626}=\frac{25250}{26260}\)
Vì \(\frac{25250}{26260}< \frac{25251}{26261}\)
\(\Rightarrow\frac{25}{26}< \frac{25251}{26261}\)
\(\left\{\begin{matrix}A=\frac{25}{26}\\B=\frac{25251}{26261}\end{matrix}\right.\)
\(\frac{25}{26}=\frac{25.1010}{26.1010}=\frac{25250}{26260}\)
\(A-B=\frac{25250}{25250}-\frac{25251}{26261}=\frac{25250.26261-25251.26260}{25250.26261}=\frac{\left(25251-1\right)\left(26260+1\right)-25251.2620}{25250.26261}\)
\(A-B=\frac{25251.26260-2-25251.2620}{25250.26261}=-\frac{2}{25250.26261}< 0\)
\(A-B< 0\Rightarrow A< B\)
Ta có: \(1-\frac{25}{26}\)\(=\frac{1}{26}\)
Lại có: \(1-\frac{25251}{26261}\)\(=\frac{1010}{26261}\)
Vậy ta so sánh: \(\frac{1}{26}\)với \(\frac{1010}{26261}\)
Quy đồng \(\frac{1}{26}\)ta có: \(\frac{1}{26}=\frac{1010}{26260}\)
Do 26260 < 26261 \(\Rightarrow\)\(\frac{1010}{26260}>\frac{1010}{26261}\)\(\Rightarrow\)\(\frac{1}{26}>\frac{1010}{26261}\)
\(\Rightarrow\frac{25}{26}< \frac{25251}{26261}\)
Duyệt đi, chúc bạn học giỏi!
vì 25/26=25250/26260 nên 25251/26261>25250/26260 vậy 25251/26261>25/26 hoặc cậu lấy máy tính bấm 25251/26261 - 25/26 còn dư nghĩa là 25251/26261>25/26 hoặc ngược lại
a) \(\dfrac{-1}{-4}\)=\(\dfrac{1}{4}>0\)
\(\dfrac{3}{-4}< 0\)
\(\Rightarrow\dfrac{1}{4}>\dfrac{3}{-4}hay\dfrac{-1}{-4}>\dfrac{3}{-4}\)
b) Ta có:
\(\dfrac{15}{17}=1-\dfrac{2}{17}\\ \)
\(\dfrac{25}{27}=1-\dfrac{2}{27}\\ \\ \)
Mà \(\dfrac{2}{17}>\dfrac{2}{27}\left(17< 27\right)\)
\(\Rightarrow1-\dfrac{2}{17}< 1-\dfrac{2}{27}\)hay \(\dfrac{15}{17}< \dfrac{25}{27}\)
a: =>2/3x=1/10+1/2=1/10+5/10=6/10=3/5
=>x=3/5:2/3=3/5x3/2=9/10
b: \(\Leftrightarrow x\cdot2.8-50=34\)
=>2,8x=84
=>x=30
c: \(\Leftrightarrow\dfrac{1}{6}x=\dfrac{5}{12}\)
hay x=5/2
d: \(\Leftrightarrow\left|2x-\dfrac{3}{4}\right|=\dfrac{17}{2}+\dfrac{7}{4}=\dfrac{41}{4}\)
=>2x-3/4=41/4 hoặc 2x-3/4=-41/4
=>2x=44/4=11 hoặc 2x=-19/2
=>x=11/2 hoặc x=-19/4
\(\left(x+\dfrac{1}{5}\right)^2+\dfrac{17}{25}=\dfrac{26}{25}\Leftrightarrow\left(x+\dfrac{1}{5}\right)^2=\dfrac{26}{25}-\dfrac{17}{25}=\dfrac{9}{25}\) \(\Leftrightarrow\left\{{}\begin{matrix}x+\dfrac{1}{5}=\dfrac{3}{5}\\x+\dfrac{1}{5}=\dfrac{-3}{5}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{5}-\dfrac{1}{5}\\x=\dfrac{-3}{5}-\dfrac{1}{5}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{5}\\x=\dfrac{-4}{5}\end{matrix}\right.\)
vậy \(x=\dfrac{2}{5};x-\dfrac{-4}{5}\)
\(\dfrac{25}{26}=\dfrac{25\cdot1010}{26\cdot1010}=\dfrac{25250}{26260}\)
Áp dụng khi \(\dfrac{a}{b}< 1\) thì \(\dfrac{a+m}{b+m}>\dfrac{a}{b}\left(m\in N^{\circledast}\right)\)
\(\dfrac{25}{26}=\dfrac{25250}{26260}< \dfrac{25250+1}{26260+1}=\dfrac{25251}{26261}\)
Vậy \(\dfrac{25}{26}< \dfrac{25251}{26261}\)
Ta có : \(\dfrac{25}{26}=\dfrac{25.101}{16.101}=\dfrac{2525}{2626}=\dfrac{25250}{26260}\)
Áp dụng công thức :
\(\dfrac{a}{b}< 1\) và \(m\in\) N, \(m\ne0\), nên
\(\dfrac{a}{b}< \dfrac{a+m}{b+m}\)
\(\Rightarrow\dfrac{25}{26}=\dfrac{25250}{26260}< \dfrac{25250+1}{26260+1}=\dfrac{25251}{26261}\)
Vậy \(\dfrac{25}{26}< \dfrac{25251}{26261}\)
~ Học tốt ~