a: Ta có: \(\left(x-\dfrac{2}{5}\right)\left(x+\dfrac{2}{7}\right)>0\)

\(\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{2}{5}\\x< -\dfrac{2}{7}\end{matrix}\right.\)

ĐKXĐ: \(x\ge3\)

\(\Leftrightarrow\sqrt{x-3}=2\sqrt{x^2-9}\)

\(\Leftrightarrow x-3=4\left(x-3\right)\left(x+3\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\4\left(x+3\right)=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{11}{4}\left(loại\right)\end{matrix}\right.\)

\(\left(2x-3\right)\left(x-\dfrac{1}{2}\right)=0\\ \Rightarrow\left[{}\begin{matrix}2x-3=0\\x-\dfrac{1}{2}=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=3\\x=\dfrac{1}{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\) (Thêm KL cuối dòng: Vậy \(x\in\left\{\dfrac{3}{2};\dfrac{1}{2}\right\}\))

(2x-3)x(x-1/2)=0

Đặt từng nhân tử bằng không và giải cho x:

2x - 3 = 0

2x = 3

x = 3/2

x = 0

x - 1/2 = 0

x = 1/2

\(1,\)

\(2x\left(x-3\right)-\left(3-x\right)=0\)

\(\Leftrightarrow2x\left(x-3\right)+\left(x-3\right)=0\)

\(\Leftrightarrow\left(2x+1\right)\left(x-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}2x+1=0\\x-3=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=3\end{cases}}\)

\(2,\)

\(3x\left(x+5\right)-6\left(x+5\right)=0\)

\(\Leftrightarrow\left(3x-6\right)\left(x+5\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3x-6=0\\x+5=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=-5\end{cases}}\)

\(3,\)

\(x^4-x^2=0\)

\(\Leftrightarrow x^2\left(x^2-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x^2=0\\x^2-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}\)

\(4,\)

\(x^2-2x=0\)

\(\Leftrightarrow x\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-2=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\)

\(5,\)

\(x\left(x+6\right)-10\left(x-6\right)=0\)

\(\Leftrightarrow x^2+6x-10x+60=0\)

\(\Leftrightarrow x^2-4x+60=0\)

\(\Leftrightarrow x^2-4x+4+56=0\)

\(\Leftrightarrow\left(x-2\right)^2=-56\)(Vô lý)

=> Phương trình vô nghiệm

\(\left(x-1\right)\left(x+2\right)\left(x-3\right)=0\)

\(\Leftrightarrow\)x - 1 = 0 hoặc x + 2 = 0 hoặc x - 3 = 0

<=> x = 1 hoặc x = -2 hoặc x = 3

Vậy \(x\in\left\{-2;1;3\right\}\)

1.A. Ta thấy để hàm số xác định thì x-m\(\ne\)0 hay x\(\ne\)m mà vì x\(\in\)(0,1) nên để x\(\ne\)m thì m\(\notin\)(0,1)=>m>=1 hoặc m<=0

2A để A giao B khác 0 thì 2m-1<=m+3 hay m<=4

3C.A giao B =A khi \(\left\{{}\begin{matrix}m< =-1\\m+5>=3\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}m< =1\\m>=-2\end{matrix}\right.\)

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

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x+3=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-3\end{cases}}\)

Vậy \(x\in\left\{0;-3\right\}\)

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

\(\Rightarrow\hept{\begin{cases}x=0\\x+3=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=0\\x=-3\end{cases}}}\)

vậy \(x=0\)hoặc\(x=-3\)

x.(x + 3) = 0

\(\Rightarrow\orbr{\begin{cases}x=0\\x+3=0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=0\\x=0-3\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=0\\x=-3\end{cases}}\)

Vậy x = 0 hoặc x = - 3