ĐKXĐ: \(x\ge-\frac{1}{2}\)
\(\Leftrightarrow x\left(x\sqrt{2x+1}-x-x-m\sqrt{2x+1}+2m\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x\sqrt{2x+1}-2x-m\sqrt{2x+1}+2m=0\left(1\right)\end{matrix}\right.\)
Xét (1):
\(\Leftrightarrow x\left(\sqrt{2x+1}-2\right)-m\left(\sqrt{2x+1}-2\right)=0\)
\(\Leftrightarrow\left(x-m\right)\left(\sqrt{2x+1}-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-m=0\\\sqrt{2x+1}-2=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=m\\x=\frac{3}{2}\end{matrix}\right.\)
Để pt đã cho có 3 nghiệm pb
\(\Leftrightarrow\left[{}\begin{matrix}m\ge-\frac{1}{2}\\m\ne0\\m\ne\frac{3}{2}\end{matrix}\right.\) \(\Rightarrow m=\left\{1;2;3;4;5;6;7;8;9\right\}\)
Có 9 giá trị thỏa mãn
