Đáp án+Giải thích các bước giải:
`5) x^2=-4x^3`
`<=> x^2+4x^3=0`
`<=> x^2(1+4x)=0`
`<=>` \(\left[ \begin{array}{l}x^{2}=0\\1+4x=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=0\\4x=-1\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=0\\x=\dfrac{-1}{4}\end{array} \right.\)
Vậy `S={0; -1/4}`
`6) x^3+8x=0`
`<=> x(x^2+8)=0`
`<=> `\(\left[ \begin{array}{l}x=0\\x^{2}+8=0\end{array} \right.\)
`<=> `\(\left[ \begin{array}{l}x=0\\x^{2}=-8(vô nghiệm)\end{array} \right.\)
Vậy `S={0}`
`7) 3x^3-27x=0`
`<=> 3x(x^2-9)=0`
`<=> `\(\left[ \begin{array}{l}3x=0\\x^{2}-9=0\end{array} \right.\)
`<=> `\(\left[ \begin{array}{l}x=0\\x^{2}=9\end{array} \right.\)
`<=> `\(\left[ \begin{array}{l}x=0\\x=±3\end{array} \right.\)
Vậy `S={0; ±3}`
`8) 4x^4+x^2=0`
`<=> x^2(4x^2+1)=0`
`<=>`\(\left[ \begin{array}{l}x^{2}=0\\4x^{2}+1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\4x^{2}=-1(vô nghiệm)\end{array} \right.\)
Vậy `S={0}`
`9) -x^3-3x=0`
`<=> -x(x^2+3)=0`
`<=>`\(\left[ \begin{array}{l}-x=0\\x^{2}+3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\x^{2}=-3(vô nghiệm)\end{array} \right.\)
Vậy `S={0}`
`10) 3x^3-9x=0`
`<=> 3x(x^2-3)=0`
`<=> ` \(\left[ \begin{array}{l}3x=0\\x^{2}-3=0\end{array} \right.\)
`<=> ` \(\left[ \begin{array}{l}x=0\\x^{2}=3\end{array} \right.\)
`<=> ` \(\left[ \begin{array}{l}x=0\\x=±\sqrt{3}\end{array} \right.\)
Vậy `S={0; ±\sqrt{3}}`
