Question

Giải các phương trình sau :

a) \(3x^3+6x^2-4x=0\)

b) \(\left(x+1\right)^3-x+1=\left(x-1\right)\left(x-2\right)\)

c) \(\left(x^2+x+1\right)^2=\left(4x-1\right)^2\)

d) \(\left(x^2+3x+2\right)^2=6\left(x^2+3x+2\right)\)

e) \(\left(2x^2+3\right)^2-10x^3-15x=0\)

f) \(x^3-5x^2-x+5=0\)

Answer 1

a) \(3x^3+6x^2-4x=0\) \(\Leftrightarrow\) \(x\left(3x^2+6x-4\right)=0\)

\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=0\\3x^2+6x-4=0\end{matrix}\right.\) \(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=0\\\left\{{}\begin{matrix}x=\dfrac{-3+\sqrt{21}}{3}\\x=\dfrac{-3-\sqrt{21}}{3}\end{matrix}\right.\end{matrix}\right.\)

vậy phương trình có 2 nghiệm \(x=0;x=\dfrac{-3+\sqrt{21}}{3};x=\dfrac{-3-\sqrt{21}}{3}\)