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Bài 3:
b: \(\Leftrightarrow\left(x-3\right)\left(x+3\right)=0\)
hay \(x\in\left\{3;-3\right\}\)
e: Để 4n+1/3n-1 là số nguyên thì \(12n+3⋮3n-1\)
\(\Leftrightarrow3n-1\in\left\{1;-1;7;-7\right\}\)
hay \(n\in\left\{0;-2\right\}\)
Bài 3:
\(a,\left(5x-2\right)+\left(-3x+1\right)=\left(-42\right)-\left(-91\right)\\ \Rightarrow5x-2+\left(-3x\right)+1=50\\ \Rightarrow2x-1=49\\ \Rightarrow2x=50\\ \Rightarrow x=25\\ b,\left(3-x\right)\left(9+3x\right)=0\\ \Rightarrow\left[{}\begin{matrix}3-x=0\\9+3x=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\3x=-9\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
\(c,5x^2-\left(-6\right)=\left(-33\right)-\left(-44\right)\\ \Rightarrow5x^2+6=11\\ \Rightarrow5x^2=5\\ \Rightarrow x^2=1\\ \Rightarrow\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)
\(d,2\left(2x-4\right)^2-77=-45\\ \Rightarrow2\left(2x-4\right)^2=32\\ \Rightarrow\left(2x-4\right)^2=16\\ \Rightarrow\left[{}\begin{matrix}2x-4=-4\\2x-4=4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=0\\2x=8\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)
a: \(-\dfrac{6}{13}=-\dfrac{12}{26}=\dfrac{-18}{39}=-\dfrac{24}{52}=\dfrac{-30}{65}=\dfrac{-36}{78}=\dfrac{-42}{91}\)
b: \(\dfrac{15}{-7}=\dfrac{-15}{7}=\dfrac{-30}{14}=\dfrac{-45}{21}=\dfrac{-60}{28}=\dfrac{-75}{35}=-\dfrac{90}{42}\)
Bài 4:
d: \(\Leftrightarrow n+2\in\left\{1;-1;2;-2;4;-4\right\}\)
hay \(n\in\left\{-1;-3;0;-4;2;-6\right\}\)