a)
Theo bài ra ta có :
\(\left(x+7\right)\left(3x-1\right)-x^2+49=0\)
\(\Leftrightarrow\left(x+7\right)\left(3x-1\right)-\left(x^2-49\right)=0\)
\(\Leftrightarrow\left(x+7\right)\left(3x-1\right)-\left(\left(x-7\right)\left(x+7\right)\right)=0\)
\(\Leftrightarrow\left(x+7\right)\left(3x-1-x+7\right)=0\)
\(\Leftrightarrow\left(x+7\right)\left(2x+6\right)=0\)
\(\Leftrightarrow\left[\begin{matrix}x+7=0\\2x+6=0\end{matrix}\right.\)
\(\Leftrightarrow\left[\begin{matrix}x=-7\\x=-3\end{matrix}\right.\)
Vậy \(S=\left\{-3;-7\right\}\)
Chúc bạn học tốt =))
a/
<=>(x+7)(3x-1)-(x^2-7^2)=0
<=>(x+7)(3x-1)-(x-7)(x+7)=0
<=>(x+7)(3x-1-x+7)=0
<=>(x+7)(2x+6)=0
<=>x+7=0 hoặc 2x+6=0
<=>x=-7 2x=-6
<=> x=-3
=>S (-7;-3)
Cho hỏi cái đề câu b là đây hả:
\(\frac{x^2-3x+1}{x^2}-\frac{3}{x}=-4\)
ĐKXĐ: \(x\ne0\)
\(\Leftrightarrow\)\(\frac{x^2-3x+1}{x^2}-\frac{3x}{x^2}=\frac{-4x^2}{x^2}\)
\(\Leftrightarrow\)\(x^2-3x+1-3x=-4x^2\)
\(\Leftrightarrow x^2+4x^2-6x+1=0\)
\(\Leftrightarrow5x^2-6x+1=0\)
\(\Leftrightarrow5x^2-5x-x+1=0\)
\(\Leftrightarrow5x\left(x-1\right)-\left(x-1\right)=0\)
\(\Leftrightarrow\left(5x-1\right)\left(x-1\right)=0\left[\begin{matrix}5x-1=0\Rightarrow x=0,2\\x-1=0\Rightarrow x=1\end{matrix}\right.\)