\(\left(x^2+2\right)^2-\left(x+2\right)\left(x-2\right)\left(x^2+4\right)=24\)
\(\Leftrightarrow x^4+4x^2+4-\left(x^2-4\right)\left(x^2+4\right)=24\)
\(\Leftrightarrow x^4+4x^2+4-\left(x^4-16\right)=24\)
\(\Leftrightarrow x^4+4x^2+4-x^4+16=24\)
\(\Leftrightarrow4x^2+20=24\)
\(\Leftrightarrow4x^2=4\)
\(\Leftrightarrow x^2=1\)
\(\Leftrightarrow x=\pm1\)
Vậy \(x=\pm1\)
\(\left(x^2+2\right)^2-\left(x+2\right)\left(x-2\right)\left(x^2+4\right)=24\)
\(\Leftrightarrow x^4+4x^2+4-\left(x^2-4\right)\left(x^2+4\right)=24\)
\(\Leftrightarrow x^4+4x^2+4-\left(x^4-16\right)=24\)
\(\Leftrightarrow x^4+4x^2+4x-x^4+16=24\)
\(\Leftrightarrow4x^2+4x+16=24\)
\(\Leftrightarrow\left(2x\right)^2+2.2x+1+15=24\)
\(\Leftrightarrow\left(2x+1\right)^2+15=24\)
\(\Leftrightarrow\left(2x+1\right)^2=9\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+1=3\\2x+1=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=2\\2x=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
