13.
\(m\left(x-m+3\right)=m\left(x-2\right)+6\)
\(\Leftrightarrow m^2-5m+6=0\)
Pt đã cho vô nghiệm khi:
\(m^2-5m+6\ne0\)
\(\Rightarrow\left\{{}\begin{matrix}m\ne2\\m\ne3\end{matrix}\right.\)
14.
\(m^2\left(x-1\right)=4x+5m+4\)
\(\Leftrightarrow\left(m^2-4\right)x=m^2+5m+4\)
\(\Rightarrow x=\dfrac{m^2+5m+4}{m^2-4}\)
Pt có nghiệm âm khi:
\(\dfrac{m^2+5m+4}{m^2-4}< 0\)
\(\Rightarrow\left[{}\begin{matrix}-4< m< -2\\-1< m< 2\end{matrix}\right.\)
15.
\(\left(m-1\right)x=m-2\)
\(\Rightarrow x=\dfrac{m-2}{m-1}\)
Pt có nghiệm âm khi:
\(\dfrac{m-2}{m-1}< 0\Rightarrow1< m< 2\)
16.
Đồ thị hai hàm số đã cho trùng nhau khi:
\(\left\{{}\begin{matrix}m+1=3m^2-1\\1=m\end{matrix}\right.\) \(\Rightarrow m=1\)
17.
\(\left(2m-1\right)x+m=0\Rightarrow x=\dfrac{m}{1-2m}\)
Pt có nghiệm trên \(\left[-1;2\right]\) khi:
\(-1\le\dfrac{m}{1-2m}\le2\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{m}{1-2m}+1\ge0\\\dfrac{m}{1-2m}-2\le0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1-m}{1-2m}\ge0\\\dfrac{5m-2}{1-2m}\le0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}m\ge1\\m< \dfrac{1}{2}\end{matrix}\right.\\\left[{}\begin{matrix}m\le\dfrac{2}{5}\\m>\dfrac{1}{2}\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}m\ge1\\m\le\dfrac{2}{5}\end{matrix}\right.\)
18.
Hai đồ thị cắt nhau khi:
\(\left(m+1\right)^2\ne3m+7\)
\(\Leftrightarrow m^2-m-6\ne0\)
\(\Rightarrow m\ne\left\{-2;3\right\}\)
19.
Gọi tuổi minh là x thì tuổi mẹ là \(x+25\)
\(\Rightarrow x+21=6\left(x-4\right)\)
\(\Rightarrow x=9\)
20.
\(\dfrac{2mx-1}{x+1}=3\Rightarrow2mx-1=3x+3\)
\(\Rightarrow\left(2m-3\right)x=4\)
\(\Rightarrow x=\dfrac{4}{2m-3}\)
Pt có nghiệm duy nhất khi: \(\left\{{}\begin{matrix}2m-3\ne0\\\dfrac{4}{2m-3}\ne-1\end{matrix}\right.\)
\(\Rightarrow m\ne\left\{-\dfrac{1}{2};\dfrac{3}{2}\right\}\)
21.
ĐKXĐ: \(x\ne\left\{1;2\right\}\)
\(\dfrac{2x-3m}{x-2}+\dfrac{x+2}{x-1}=3\)
\(\Rightarrow\left(2x-3m\right)\left(x-1\right)+\left(x-2\right)\left(x+2\right)=3\left(x-2\right)\left(x-1\right)\)
\(\Leftrightarrow\left(3m-7\right)x=3m-10\)
\(\Rightarrow x=\dfrac{3m-10}{3m-7}\)
Pt vô nghiệm khi:
\(\left[{}\begin{matrix}3m-7=0\\\dfrac{3m-10}{3m-7}=1\\\dfrac{3m-10}{3m-7}=2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}m=\dfrac{7}{3}\\m=\dfrac{4}{3}\end{matrix}\right.\)
\(\Rightarrow\left(\dfrac{7}{3}\right)^2+\left(\dfrac{4}{3}\right)^2=\dfrac{65}{9}\)
22.
\(\left(x+1\right)\left(x+a+2\right)-x\left(x-a+1\right)=0\)
\(\Rightarrow\left(2a+2\right)x=-a-2\)
\(\Rightarrow x=\dfrac{-a-2}{2a+2}\)
Pt vô nghiệm khi: \(\left[{}\begin{matrix}2a+2=0\\\dfrac{-a-2}{2a+2}=a-1\\\dfrac{-a-2}{2a+2}=-a-2\end{matrix}\right.\)
\(\Rightarrow a=\left\{-\dfrac{1}{2};0;-2;-1\right\}\)
