\(3x^4+x^2-4=0\)
\(\Leftrightarrow3x^4-3x^2+4x^2-4=0\)
\(\Leftrightarrow3x^2\cdot\left(x^2-1\right)+4\cdot\left(x^2-1\right)=0\)
\(\Leftrightarrow\left(x^2-1\right)\left(3x^2+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-1=0\\3x^2+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\pm1\\x^2=-\dfrac{4}{3}\left(l\right)\end{matrix}\right.\)
\(S=\left\{\pm1\right\}\)
Đặt `x^2=t(t>=0)`
Ta có PT: `3t^2+t-4=0`
`3+1-4=0`
`=> t_1 = 1 ; t_2 = -4/3 (L)`
`=> x^2=1`
`<=> x=\pm 1`
Vậy `S={\pm 1}`.
\(3x^4+x^2-4=0\\ \Leftrightarrow3x^4-3x^2+4x^2-4=0\\ \Leftrightarrow3x^2\left(x^2-1\right)+4\left(x^2-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+1\right)\left(3x^2+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\\3x^2+4>0\forall x\end{matrix}\right.\)
Vậy \(S=\left\{-1;1\right\}\) là tập nghiệm của pt
