Bài 3: Giải phương trình:
a) x3+ 2x2 + x +2 = 0
b) x3 – x2 – 21x + 45 = 0
c) x3 + 3x2+4x + 2 = 0
d) x4+ x2 +6x – 8 = 0
e) (x2 + 1)2 = 4 ( 2x – 1 )
Bài 4: Giải phương trình:
a) ( x2-5x)2 + 10( x2 – 5x) + 24 = 0
b) ( x2 + 5x)2 - 2( x2 + 5x) = 24
c) ( x2 + x – 2)(x2 + x – 3) = 12
d) x ( x+1) (x2 + x + 1) = 42
Bài 1
a/ \(x\left(x^2+1\right)+2\left(x^2+1\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^2+1\right)=0\Rightarrow x=-2\)
b/
\(\Leftrightarrow x^3-6x^2+9x+5x^2-30x+45=0\)
\(\Leftrightarrow x\left(x-3\right)^2+5\left(x-3\right)^2=0\)
\(\Leftrightarrow\left(x+5\right)\left(x-3\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-5\\x=3\end{matrix}\right.\)
1.
c/ \(\Leftrightarrow x^3+2x^2+2x+x^2+2x+2=0\)
\(\Leftrightarrow x\left(x^2+2x+2\right)+x^2+2x+2=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2+2x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x^2+2x+2=0\left(vn\right)\end{matrix}\right.\)
d/
\(\Leftrightarrow x^4+x^3-2x^2-x^3-x^2+2x+4x^2+4x-8=0\)
\(\Leftrightarrow x^2\left(x^2+x-2\right)-x\left(x^2+x-2\right)+4\left(x^2+x-2\right)=0\)
\(\Leftrightarrow\left(x^2-x+4\right)\left(x^2+x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-x+4=0\left(vn\right)\\x^2+x-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
Bài 1:
e/ \(\Leftrightarrow x^4+2x^2-8x+5=0\)
\(\Leftrightarrow x^4-2x^3+x^2+2x^3-4x^2+2x+5x^2-10x+5=0\)
\(\Leftrightarrow x^2\left(x-1\right)^2+2x\left(x-1\right)^2+5\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(x^2+2x+5\right)\left(x-1\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+2x+5=0\left(vn\right)\\x=1\end{matrix}\right.\)
Bài 2:
a/ Đặt \(x^2-5x=t\)
\(t^2+10t+24=0\Rightarrow\left[{}\begin{matrix}t=-4\\t=-6\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-5x=-4\\x^2-5x=-6\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-5x+4=0\\x^2-5x+6=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=4\\x=2\\x=3\end{matrix}\right.\)
Bài 2:
b/ Đặt \(x^2+5x=t\)
\(t^2-2t-24=0\Rightarrow\left[{}\begin{matrix}t=6\\t=-4\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2+5x=6\\x^2+5x=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+5x-6=0\\x^2+5x+4=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=-6\\x=-1\\x=-4\end{matrix}\right.\)
c/ Đặt \(x^2+x-2=t\)
\(\Leftrightarrow t\left(t-1\right)-12=0\)
\(\Leftrightarrow t^2-t-12=0\Rightarrow\left[{}\begin{matrix}t=4\\t=-3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2+x-2=4\\x^2+x-2=-3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x^2+x-6=0\left(casio\right)\\x^2+x+1=0\left(vn\right)\end{matrix}\right.\)
d/ \(\Leftrightarrow\left(x^2+x\right)\left(x^2+x+1\right)-42=0\)
Đặt \(x^2+x=t\)
\(t\left(t+1\right)-42=0\Leftrightarrow t^2+t-42=0\Rightarrow\left[{}\begin{matrix}t=6\\t=-7\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2+x-6=0\left(casio\right)\\x^2+x+7=0\left(vn\right)\end{matrix}\right.\)
