Question

giải pt trên:

\(x^4+x^3+6x^2=-5\left(x+1\right)\)

Answer 1

\(x^4+x^3+6x^2=-5\left(x+1\right)\)

\(\Leftrightarrow x^4+x^3+6x^2+5x+5=0\)

\(\Leftrightarrow x^4+x^3+x^2+5x^2+5x+5=0\)

\(\Leftrightarrow x^2\left(x^2+x+1\right)+5\left(x^2+x+1\right)=0\)

\(\Leftrightarrow\left(x^2+5\right)\left(x^2+x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2+5=0\\x^2+x+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2=-5\\\left(x+\dfrac{1}{2}\right)^2=-\dfrac{3}{4}\end{matrix}\right.\)(vô lí)

-Vậy S=∅