Question

1) tìm x , biết

a) x(x-3)+x-3=0

b) 7x(x-1) -x+1=0

Answer 1

a) \(\Rightarrow x\left(x-3\right)+\left(x-3\right)=0\)

\(\Rightarrow\left(x+1\right)\left(x-3\right)=0\)

\(\Rightarrow\left\{{}\begin{matrix}x+1=0\\x-3=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=-1\\x=3\end{matrix}\right.\).

b) \(\Rightarrow7x\left(x-1\right)-\left(x-1\right)=0\)

\(\Rightarrow\left(7x-1\right)\left(x-1\right)=0\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{1}{7}\\x=1\end{matrix}\right.\).

Answer 2

a) \(x\left(x-3\right)+x-3=0\) (1)

\(\Leftrightarrow x\left(x-3\right)+\left(x-3\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-3=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=3\end{matrix}\right.\)

Vậy tập nghiệm phương trình (1) là \(S=\left\{-1;3\right\}\)

b) \(7x\left(x-1\right)-x+1=0\) (2)

\(\Leftrightarrow7x\left(x-1\right)-\left(x-1\right)=0\)

\(\Leftrightarrow\left(7x-1\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}7x-1=0\\x-1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{7}\\x=1\end{matrix}\right.\)

Vậy tập nghiệm phương trình (2) là \(S=\left\{\dfrac{1}{7};1\right\}\)

Answer 3

Câu a : \(x\left(x-3\right)+x-3=0\)

\(\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\Rightarrow x=3\\x+1=0\Rightarrow x=1\end{matrix}\right.\)

Câu b : \(7x\left(x-1\right)-x+1=0\)

\(\Leftrightarrow7x\left(x-1\right)-\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(7x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\Rightarrow x=1\\7x-1=0\Rightarrow x=\dfrac{1}{7}\end{matrix}\right.\)

Answer 4

\(x\left(x-3\right)+x-3=0\)

\(\Rightarrow\left(x+1\right)\left(x-3\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x+1=0\\x-3=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=-1\\x=3\end{matrix}\right.\)

\(7x\left(x-1\right)-x+1=0\)

\(\Rightarrow7x\left(x-1\right)-x-1+2=0\)

\(\Rightarrow\left(7x-1\right)\left(x-1\right)+2=0\)

\(\Rightarrow\left(7x-1\right)\left(x-1\right)=-2\)