Question

giải phương trình

\(4t^4+4t^3+3t^2+t=0\)

Answer 1

\(4t^4+4t^3+3t^2+t=0\)

\(\Leftrightarrow t\left(4t^3+4t^2+3t+1\right)=0\)

\(\Leftrightarrow t\left(4t^3+2t^2+2t^2+t+2t+1\right)=0\)

\(\Leftrightarrow t\left[2t^2\left(2t+1\right)+t\left(2t+1\right)+\left(2t+1\right)\right]=0\)

\(\Leftrightarrow t\left(2t+1\right)\left(2t^2+t+1\right)=0\)

Vì \(2t^2+t+1>0\forall t\)

\(\Leftrightarrow\left[{}\begin{matrix}t=0\\2t+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}t=0\\t=\frac{-1}{2}\end{matrix}\right.\)