bài 2 câu 1,2,3,5,9
2.1
\(\Leftrightarrow x^3+3x^2+2x-3x^2-9x-6=0\)
\(=x\left(x^2+3x+2\right)-3\left(x^2+3x+2\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x^2+3x+2\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+1\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\\x=-2\end{matrix}\right.\)
2.2
\(\Leftrightarrow x^3-2x^2-2x-x^2+2x+2=0\)
\(\Leftrightarrow x\left(x^2-2x-2\right)-\left(x^2-2x-2\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-2x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=1\pm\sqrt{3}\end{matrix}\right.\)
2.3
\(\Leftrightarrow3x^3-3x^2+2x+3x^2-3x+2=0\)
\(\Leftrightarrow x\left(3x^2-3x+2\right)+3x^2-3x+2=0\)
\(\Leftrightarrow\left(x+1\right)\left(3x^2-3x+2\right)=0\)
\(\Leftrightarrow x=-1\)
2.5
\(\Leftrightarrow2x^3+x^2+3x-4x^2-2x-6=0\)
\(\Leftrightarrow x\left(2x^2+x+3\right)-2\left(2x^2+x+3\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(2x^2+x+3\right)=0\)
\(\Leftrightarrow x=2\)
2.9
\(\Leftrightarrow3x^3-3x^2-3x=1\)
\(\Leftrightarrow3x^3=3x^2+3x+1\)
\(\Leftrightarrow4x^3=x^3+3x^2+3x+1\)
\(\Leftrightarrow4x^3=\left(x+1\right)^3\)
\(\Leftrightarrow\left(x\sqrt[3]{4}\right)^3=\left(x+1\right)^3\)
\(\Leftrightarrow x\sqrt[3]{4}=x+1\)
\(\Leftrightarrow x\left(\sqrt[3]{4}-1\right)=1\)
\(\Leftrightarrow x=\dfrac{1}{\sqrt[3]{4}-1}\)
3.1
\(\Leftrightarrow x^4-3x^2-2x^2+6=0\)
\(\Leftrightarrow x^2\left(x^2-3\right)-2\left(x^2-3\right)=0\)
\(\Leftrightarrow\left(x^2-2\right)\left(x^2-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=2\\x^2=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\pm\sqrt{2}\\x=\pm\sqrt{3}\end{matrix}\right.\)
3.5
Đặt \(7-x=t\) pt trở thành:
\(\left(t-1\right)^4+\left(t+1\right)^4=16\)
\(\Leftrightarrow t^4+6t^2-7=0\)
\(\Leftrightarrow t^4-t^2+7t^2-7=0\)
\(\Leftrightarrow t^2\left(t^2-1\right)+7\left(t^2-1\right)=0\)
\(\Leftrightarrow\left(t^2-1\right)\left(t^2+7\right)=0\)
\(\Leftrightarrow t^2=1\Rightarrow\left[{}\begin{matrix}t=1\\t=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}7-x=1\\7-x=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=6\\x=8\end{matrix}\right.\)
