Bài 1 :
a)
\(\dfrac{1}{2}.\sqrt{100}-\sqrt{\dfrac{1}{25}}+\left(-\dfrac{1}{4}\right)^0\)
\(=\dfrac{1}{2}.10-\dfrac{1}{5}+1\)
\(=5-\dfrac{1}{5}+1\)
\(=\dfrac{24}{5}+1\)
\(=\dfrac{29}{5}\)
b)
\(\dfrac{13}{25}+\dfrac{7}{41}-\left(\dfrac{38}{25}-\dfrac{34}{41}-\dfrac{1}{2}\right)\)
\(=\dfrac{13}{25}+\dfrac{7}{41}-\dfrac{38}{25}+\dfrac{34}{41}+\dfrac{1}{2}\)
\(=\left(\dfrac{13}{25}-\dfrac{38}{25}\right)+\left(\dfrac{7}{41}+\dfrac{34}{41}\right)+\dfrac{1}{2}\)
\(=-1+1+\dfrac{1}{2}\)
\(=0+\dfrac{1}{2}\)
\(=\dfrac{1}{2}\)
Bài 2 :
a)
\(\dfrac{13}{4}-\left(x+\dfrac{1}{7}\right)=\dfrac{3}{4}\)
\(x+\dfrac{1}{7}=\dfrac{13}{4}-\dfrac{3}{4}\)
\(x+\dfrac{1}{7}=\dfrac{5}{2}\)
\(x=\dfrac{5}{2}-\dfrac{1}{7}\)
\(x=\dfrac{35}{14}-\dfrac{2}{14}\)
\(x=\dfrac{33}{14}\)
Vậy \(x=\dfrac{33}{14}\)
b)
\(\left(2x-1\right)^2=\dfrac{4}{9}\)
\(\left(2x-1\right)^2=\left(\dfrac{2}{3}\right)^2\) hoặc \(\left(-\dfrac{2}{3}\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}2x-1=\dfrac{2}{3}\\2x-1=\dfrac{-2}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=\dfrac{2}{3}+1\\2x=\dfrac{-2}{3}+1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=\dfrac{5}{3}\\2x=\dfrac{1}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}:2\\x=\dfrac{1}{3}:2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{6}\\x=\dfrac{1}{6}\end{matrix}\right.\)
Vậy \(x=\dfrac{5}{6};x=\dfrac{1}{6}\)
1.
a)\(\dfrac{1}{2}.\sqrt{100}-\sqrt{\dfrac{1}{25}}+\left(-\dfrac{1}{4}\right)^0\)
\(=\dfrac{1}{2}.10-\dfrac{1}{5}+1=5-\dfrac{1}{5}+\dfrac{5}{5}=\dfrac{25}{5}-\dfrac{1}{5}+\dfrac{5}{5}=\dfrac{29}{5}\)
b)\(\dfrac{13}{25}+\dfrac{7}{41}-\left(\dfrac{38}{25}-\dfrac{34}{41}-\dfrac{1}{2}\right)\)
\(=\dfrac{13}{25}+\dfrac{7}{41}-\dfrac{38}{25}+\dfrac{34}{41}+\dfrac{1}{2}\)
\(=\left(\dfrac{13}{25}-\dfrac{38}{25}\right)+\left(\dfrac{7}{41}+\dfrac{34}{41}\right)+\dfrac{1}{2}\)
\(=-1+1+\dfrac{1}{2}=0+\dfrac{1}{2}=\dfrac{1}{2}\)
