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\(a;\)\(\left(x+\frac{1}{3}\right)^2=x+\frac{1}{3}\)
\(\Leftrightarrow\left(x+\frac{1}{3}\right)^2-\left(x+\frac{1}{3}\right)=0\)
\(\Leftrightarrow\left(x+\frac{1}{3}\right)\left(x+\frac{1}{3}-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{3}=0\\x+\frac{1}{3}-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{3}\\x=\frac{2}{3}\end{cases}}}\)
b)\(\left(x-\frac{1}{4}\right)^3=\left(x-\frac{1}{4}\right)^2\)
\(\Leftrightarrow\left(x-\frac{1}{4}\right)^3-\left(x-\frac{1}{4}\right)^2=0\)
\(\Leftrightarrow\left(x-\frac{1}{4}\right)^2\left(x-\frac{1}{4}-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x-\frac{1}{4}\right)^2=0\\\left(x-\frac{1}{4}-1\right)=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-\frac{1}{4}=0\\x-\frac{5}{4}=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{4}\\x=\frac{5}{4}\end{cases}}}\)
a) (x + 1/2) . (2/3 − 2x) = 0
\(\Rightarrow\left[\begin{array}{nghiempt}x+\frac{1}{2}=0\\\frac{2}{3}-2x=0\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=-\frac{1}{2}\\2x=\frac{2}{3}\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=-\frac{1}{2}\\x=\frac{1}{3}\end{array}\right.\)
b) \(\left(x.6\frac{2}{7}+\frac{3}{7}\right).2\frac{1}{5}-\frac{3}{7}=-2\)
\(\Rightarrow\left(x.\frac{44}{7}+\frac{3}{7}\right).\frac{11}{5}=-2+\frac{3}{7}\)
\(\Rightarrow\left(x.\frac{44}{7}+\frac{3}{7}\right).\frac{11}{5}=-\frac{11}{7}\)
\(\Rightarrow x.\frac{44}{7}+\frac{3}{7}=-\frac{11}{7}:\frac{11}{5}=-\frac{11}{7}.\frac{5}{11}\)
\(\Rightarrow x.\frac{44}{7}+\frac{3}{7}=-\frac{5}{7}\)
\(\Rightarrow x.\frac{44}{7}=-\frac{5}{7}-\frac{3}{7}\)
\(\Rightarrow x.\frac{44}{7}=-\frac{8}{7}\)
\(\Rightarrow x=-\frac{8}{7}:\frac{44}{7}=-\frac{8}{7}.\frac{7}{44}\)
\(\Rightarrow x=-\frac{2}{11}\)
c) \(x.3\frac{1}{4}+\left(-\frac{7}{6}\right).x-1\frac{2}{3}=\frac{5}{12}\)
\(\Rightarrow x\left(3\frac{1}{4}-\frac{7}{6}\right)=\frac{5}{12}+\frac{5}{3}\)
\(\Rightarrow x\left(\frac{13}{4}-\frac{7}{6}\right)=\frac{25}{12}\)
\(\Rightarrow x.\frac{25}{12}=\frac{25}{12}\)
\(\Rightarrow x=\frac{25}{12}:\frac{25}{12}\)
\(\Rightarrow x=1\)
d) \(5\frac{8}{17}:x+\left(-\frac{4}{17}\right):x+3\frac{1}{7}:17\frac{1}{3}=\frac{4}{11}\)
\(\Rightarrow\left(5\frac{8}{17}-\frac{4}{17}\right):x+\frac{22}{7}:\frac{52}{3}=\frac{4}{11}\)
\(\Rightarrow5\frac{4}{17}:x+\frac{33}{182}=\frac{4}{11}\)
\(\Rightarrow\frac{89}{17}:x=\frac{4}{11}-\frac{33}{182}\)
\(\Rightarrow\frac{89}{17}:x=\frac{365}{2002}\)
\(\Rightarrow x=\frac{89}{17}:\frac{365}{2002}\)
\(\Rightarrow x\approx28,7\) (số hơi lẻ)
e) \(\frac{17}{2}-\left|2x-\frac{3}{4}\right|=-\frac{7}{4}\)
\(\Rightarrow\left|2x-\frac{3}{4}\right|=\frac{17}{2}+\frac{7}{4}\)
\(\Rightarrow\left|2x-\frac{3}{4}\right|=\frac{41}{4}\)
\(\Rightarrow\left[\begin{array}{nghiempt}2x-\frac{3}{4}=\frac{41}{4}\\2x-\frac{3}{4}=-\frac{41}{4}\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}2x=11\\2x=-\frac{19}{2}\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{11}{2}\\x=-\frac{19}{4}\end{array}\right.\)
\(\left(2\frac{4}{5}x-50\right)\div\frac{2}{3}=51\)
\(\frac{14}{5}x-50=51\times\frac{2}{3}\)
\(\frac{14}{5}x-50=34\)
\(\frac{14}{5}x=84\)
\(x=84\times\frac{5}{14}\)
\(x=30\)
\(a,\left(2\frac{4}{5}.x-50\right):\frac{2}{3}=51\)
\(\left(\frac{14}{5}.x-50\right):\frac{2}{3}=51\)
\(\frac{14}{5}.x-50=51\times\frac{2}{3}\)
\(\frac{14}{5}.x-50=34\)
\(\frac{14}{5}.x=34+50\)
\(\frac{14}{5}.x=84\)
\(x=84:\frac{14}{5}\)
\(x=\frac{405}{14}\)
\(\Leftrightarrow4x-1-3x-2=0\)
\(\Leftrightarrow x=0+1+2\)
\(\Leftrightarrow x=3\)
\(3\left(2x-\frac{5}{4}\right)=\left(3-1\frac{1}{2}\right)\left(x-\frac{1}{2}\right)\)
\(\Leftrightarrow6x-\frac{15}{4}=\frac{3}{2}x+\frac{1}{12}\)
\(\Leftrightarrow\frac{9}{2}x+\frac{3}{4}=\frac{15}{4}\)
\(\Leftrightarrow\frac{9}{2}x=3\)
\(\Leftrightarrow x=\frac{2}{3}\)
\(\frac{1954.0,24+76.19,54}{977.\left(x-4\right)}=2=>\frac{977.2.0,24+76.19,54}{977.\left(x-4\right)}=2\)
=> \(\frac{2.0,24+76.19,54}{x-4}=2\)
=> \(\frac{1485,52}{x-4}=2=>1485,52=\left(x-4\right).2\)
=> x - 4 = 1485,52 : 2
x - 4 =742,76
=> x = 742,76+4
=> x = 746,76
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