Đáp án + Giải thích các bước giải:

`a,x^3+x=0`

`=> x(x^2+1)=0`

\(⇒\left[ \begin{array}{l}x=0\\x^2+1=0\end{array} \right.\)

\(⇒\left[ \begin{array}{l}x=0\quad(Tm)\\x^2=-1\quad(Ktm)\end{array} \right.\)

Vậy `S={0}`

`b,2x(x-9)+3(x-9)=0`

`=> (x-9)(2x+3)=0`

\(⇒\left[ \begin{array}{l}x-9=0\\2x+3=0\end{array} \right.\)

\(⇒\left[ \begin{array}{l}x=9\\2x=-3\end{array} \right.\)

\(⇒\left[ \begin{array}{l}x=9\\x=-\dfrac{3}2\end{array} \right.\)

Vậy `S={9;-3/2}`

`c,6x^2-3x=0`

`=>3x(2x-1)=0` 

\(⇒\left[ \begin{array}{l}3x=0\\2x-1=0\end{array} \right.\)

\(⇒\left[ \begin{array}{l}x=0\\2x=1\end{array} \right.\)

\(⇒\left[ \begin{array}{l}x=0\\x=\dfrac{1}2\end{array} \right.\)

Vậy `S={0;1/2}`

`d,5x^3(7x+1)-10x^2(7x+1)=0`

`=>(7x+1)(5x^3-10x^2)=0`

`=>(7x+1)(x-2)5x^2=0`

\(⇒\left[ \begin{array}{l}7x+1=0\\x-2=0\\5x^2=0\end{array} \right.\)

\(⇒\left[ \begin{array}{l}7x=-1\\x=2\\x^2=0\end{array} \right.\)

\(⇒\left[ \begin{array}{l}x=-\dfrac{1}7\\x=2\\x=0\end{array} \right.\)

Vậy `S={-1/7;2;0}`

`x^3+x=0`

`⇒x(x^2+1)=0`

`⇒` \(\left[ \begin{array}{l}x=0\\x^2+1=0\end{array} \right.\)

`⇒` \(\left[ \begin{array}{l}x=0\\x^2=-1\text{ (loại; do x² ≥ 0)}\end{array} \right.\)

Vậy `x=0`.

`2x(x-9)+3(x-9) =0`

`⇒(2x+3)(x-9)=0`

`⇒` \(\left[ \begin{array}{l}2x+3=0\\x-9=0\end{array} \right.\)

$⇒ \left[ \begin{array}{l}x=9\\x=-\dfrac{3}2\end{array} \right.$

Vậy `x=-3/2` hoặc `x=9`.

`6x^2-3x=0`

`⇒3x(2x-1)=0`

`⇒` $\left[ \begin{array}{l}3x=0\\2x-1=0\end{array} \right.$

$⇒\left[ \begin{array}{l}x=0\\x=\dfrac{1}2\end{array} \right.$

Vậy `x=0` hoặc `x=1/2`.

`5x^3(7x+1)-10x^2(7x+1)=0`

`⇒(7x+1)(5x^3-10x^2)=0`

`⇒(7x+1)(x-2)5x^2=0`

$⇒\left[ \begin{array}{l}7x+1=0\\x-2=0\\5x^2=0\end{array} \right.$

$⇒\left[ \begin{array}{l}7x=-1\\x=2\\x^2=0\end{array} \right.$

$⇒\left[ \begin{array}{l}x=-\dfrac{1}7\\x=2\\x=0\end{array} \right.$

Vậy `x∈{-1/7;2;0}`.