\(\left(3x+2\right)\left(x^2+1\right)=\left(9x^2-4\right)\left(x+1\right)\\ \Leftrightarrow3x^3+2x^2+3x+2=9x^3+9x^2-4x-4\\\Leftrightarrow -6x^3-7x^2+7x+6=0\\\Leftrightarrow -6\left(x^3+\frac{7}{6}x^2-\frac{7}{6}x-1\right)=0\\\Leftrightarrow x^3+\frac{7}{6}x^2-\frac{7}{6}x-1=0\\\Leftrightarrow x^3-x^2+\frac{2}{3}x^2+\frac{3}{2}x^2-\frac{2}{3}x-\frac{3}{2}x+x-1=0\\\Leftrightarrow x^3-x^2+\frac{2}{3}x^2-\frac{2}{3}x+\frac{3}{2}x^2-\frac{3}{2}x+x-1=0\\ \Leftrightarrow\left(x^2+\frac{2}{3}x+\frac{3}{2}x+1\right)\left(x-1\right)=0\\\Leftrightarrow \left(x+\frac{2}{3}\right)\left(x+\frac{3}{2}\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\frac{2}{3}=0\\x+\frac{3}{2}=0\\x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\frac{2}{3}\\x=-\frac{3}{2}\\x=1\end{matrix}\right.\)
Vậy nghiệm của phương trình trên là \(S=\left\{-\frac{2}{3};-\frac{3}{2};1\right\}\)
Sửa lại đề là:
\(\left(3x+2\right).\left(x^2+1\right)=\left(9x^2-4\right).\left(x+1\right)\)
\(\Leftrightarrow\left(3x+2\right).\left(x^2+1\right)-\left(9x^2-4\right).\left(x+1\right)=0\)
\(\Leftrightarrow\left(3x+2\right).\left(x^2+1\right)-\left[\left(3x\right)^2-2^2\right].\left(x+1\right)=0\)
\(\Leftrightarrow\left(3x+2\right).\left(x^2+1\right)-\left(3x-2\right).\left(3x+2\right).\left(x+1\right)=0\)
\(\Leftrightarrow\left(3x+2\right).\left[x^2+1-\left(3x-2\right).\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(3x+2\right).\left[x^2+1-\left(3x^2+3x-2x-2\right)\right]=0\)
\(\Leftrightarrow\left(3x+2\right).\left(x^2+1-3x^2-3x+2x+2\right)=0\)
\(\Leftrightarrow\left(3x+2\right).\left(-2x^2-x+3\right)=0\)
\(\Leftrightarrow\left(3x+2\right).\left(-2x^2-3x+2x+3\right)=0\)
\(\Leftrightarrow\left(3x+2\right).\left[\left(-2x^2-3x\right)+\left(2x+3\right)\right]=0\)
\(\Leftrightarrow\left(3x+2\right).\left[-x.\left(2x+3\right)+\left(2x+3\right)\right]=0\)
\(\Leftrightarrow\left(3x+2\right).\left(2x+3\right).\left(1-x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+2=0\\2x+3=0\\1-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=-2\\2x=-3\\x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\frac{2}{3}\\x=-\frac{3}{2}\\x=1\end{matrix}\right.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{-\frac{2}{3};-\frac{3}{2};1\right\}.\)
Chúc bạn học tốt!
