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Bài làm:
c) \(\left(x-2\right)\left(x+3\right)>0\)
Ta xét 2 trường hợp sau:
+ Nếu \(\hept{\begin{cases}x-2>0\\x+3>0\end{cases}\Rightarrow}\hept{\begin{cases}x>2\\x>-3\end{cases}\Rightarrow}x>2\)
+ Nếu \(\hept{\begin{cases}x-2< 0\\x+3< 0\end{cases}}\Rightarrow\hept{\begin{cases}x< 2\\x< -3\end{cases}}\Rightarrow x< -3\)
Vậy \(\orbr{\begin{cases}x>2\\x< -3\end{cases}}\)
d) \(-1\frac{5}{27}-\left(3x-\frac{7}{9}\right)^3=-\frac{24}{27}\)
\(\Leftrightarrow-\frac{32}{27}-\left(3x-\frac{7}{9}\right)^3=-\frac{24}{27}\)
\(\Leftrightarrow\left(3x-\frac{7}{9}\right)^3=-\frac{8}{27}\)
\(\Leftrightarrow\left(3x-\frac{7}{9}\right)^3=\left(-\frac{2}{3}\right)^3\)
\(\Rightarrow3x-\frac{7}{9}=-\frac{2}{3}\)
\(\Leftrightarrow3x=\frac{1}{9}\)
\(\Leftrightarrow x=\frac{1}{27}\)
Vậy \(x=\frac{1}{27}\)
Học tốt!!!!
\(Y=\frac{\frac{1}{3}+\frac{1}{9}-\frac{1}{27}}{\frac{5}{3}+\frac{5}{9}-\frac{5}{27}}\)
\(\Rightarrow Y=\frac{\frac{1}{3}+\frac{1}{9}-\frac{1}{27}}{5\cdot\left(\frac{1}{3}+\frac{1}{9}-\frac{1}{27}\right)}\)
\(\Rightarrow Y=\frac{1}{5}\)
K CHO MH NHA
\(a\)) Giải:
\(A=\frac{\frac{1}{3}+\frac{1}{9}-\frac{1}{27}}{\frac{5}{3}+\frac{5}{9}-\frac{5}{27}}=\frac{\frac{1}{3}+\frac{1}{9}-\frac{1}{27}}{5.\left(\frac{1}{3}+\frac{1}{9}-\frac{1}{27}\right)}=\frac{1}{5}\)
\(b\)) Giải:
\(B=\frac{\frac{2}{3}-\frac{1}{4}+\frac{5}{11}}{\frac{5}{12}+1-\frac{7}{11}}=\frac{\left(\frac{2}{3}-\frac{1}{4}+\frac{5}{11}\right).132}{\left(\frac{5}{12}+1-\frac{7}{11}\right).132}=\frac{88-33+60}{55+132-84}=\frac{115}{103}\)
\((x-6)(3x-9)>0\)
TH1:
\(\orbr{\begin{cases}x-6< 0\\3x-9< 0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x< 6\\x< 3\end{cases}}\)\(\Rightarrow x< 3\)
TH2:
\(\orbr{\begin{cases}x-6>0\\3x-9>0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x>6\\x>3\end{cases}}\)\(\Rightarrow x>6\)
Vậy \(x< 3\) hoặc \(x>6\)thì \((x-6)(3x-9)>0\)
Học tốt!
20.
\((2x-1)(6-x)>0\)
TH1:
\(\orbr{\begin{cases}2x-1>0\\6-x>0\end{cases}\Rightarrow\orbr{\begin{cases}x< \frac{1}{2}\\x< 6\end{cases}}\Rightarrow x< 6}\)
TH2
\(\orbr{\begin{cases}2x-1< 0\\6-x< 0\end{cases}\Rightarrow\orbr{\begin{cases}x>\frac{1}{2}\\x>6\end{cases}}\Rightarrow x>\frac{1}{2}}\)
Vậy \(x< 6\)hoặc \(x>\frac{1}{2}\)thì \((2x-1)(6-x)>0\)
a) \(\frac{x}{5}-\frac{x}{6}=\frac{3}{10}\\ \frac{6x}{30}-\frac{5x}{30}=\frac{3\cdot3}{10\cdot3}\\ \frac{x}{30}=\frac{9}{30}\\ \Rightarrow x=9\) Vậy x = 9
b) \(-1\frac{5}{27}-\left(3x-\frac{7}{9}\right)^3=-\frac{24}{27}\\ \frac{-32}{27}+\frac{24}{27}=\left(3x-\frac{7}{9}\right)^3\\ \left(3x-\frac{7}{9}\right)^3=\frac{-8}{27}\\ \left(3x-\frac{7}{9}\right)^3=\left(\frac{-2}{3}\right)^3\\ \Rightarrow3x-\frac{7}{9}=\frac{-2}{3}\\ 3x=\frac{-2}{3}+\frac{7}{9}\\ 3x=\frac{-6}{9}+\frac{7}{9}\\ 3x=\frac{1}{9}\\ x=\frac{1}{9}:3\\ x=\frac{1}{9\cdot3}\\ x=\frac{1}{27}\)Vậy \(x=\frac{1}{27}\)
a)\(\left(x+\frac{1}{5}\right)^2+\frac{17}{25}=\frac{26}{25}\)
=\(\left(x+\frac{1}{5}\right)^2=\frac{9}{25}=\frac{3^2}{5^2}\)
=\(x+\frac{1}{5}=\frac{3}{5}\)
\(x=\frac{2}{5}\)
b)\(-1\frac{5}{27}-\left(3x-\frac{7}{9}\right)^3=\frac{24}{27}\)
=\(x=-\frac{35}{27}\)