a)\(\left(x^2-1\right)^2=4x+1\)
\(\Leftrightarrow x^4-2x^2+1=4x+1\)
\(\Leftrightarrow x^4-2x^2+1-4x-1=0\)
\(\Leftrightarrow x^4-2x^2-4x=0\)
\(\Leftrightarrow x\left(x^3-2x-4\right)=0\)
\(\Leftrightarrow x\left(x^3+2x^2+2x-2x^2-4x-4\right)=0\)
\(\Leftrightarrow x\left[x\left(x^2+2x+2\right)-2\left(x^2+2x+2\right)\right]=0\)
\(\Leftrightarrow x\left(x-2\right)\left(x^2+2x+2\right)=0\)
\(\Leftrightarrow\left[\begin{matrix}x=0\\x-2=0\\x^2+2x+2=0\end{matrix}\right.\)\(\Leftrightarrow\left[\begin{matrix}x=0\\x=2\\\left(x+1\right)^2+1>0\left(loai\right)\end{matrix}\right.\)
c)\(\left(x^2+3x\right)^2+8\left(x^2+3x\right)=48\)
Đặt \(t=x^2+3x\) ta có:
\(t^2+8t=48\Rightarrow t^2+8t-48=0\)
\(\Rightarrow\left(t+12\right)\left(t-4\right)=0\)\(\Rightarrow\left[\begin{matrix}t=-12\\t=4\end{matrix}\right.\)
*)Xét \(t=-12\Rightarrow x^2+3x=-12\)
\(\Rightarrow x^2+3x+12=0\Rightarrow\left(x+\frac{3}{2}\right)^2+\frac{39}{4}>0\left(loai\right)\)
*)Xét \(t=4\Rightarrow x^2+3x=4\)
\(\Rightarrow\left(x-1\right)\left(x+4\right)=0\)\(\Rightarrow\left[\begin{matrix}x=-4\\x=1\end{matrix}\right.\)
