Đáp án+Giải thích các bước giải:

`2)` `(9-3x)(15+3x)=0`

`<=> [(9-3x=0),(15+3x=0):}`

`<=> [(3x=9),(3x=-15):}`

`<=> [(x=3),(x=-5):}`

Vậy `S={3;-5}`

`4)`

`(x^2+x+1)(6-2x)=0`

Nhận xét: `x^2+x+1=(x+1/2)^2 +3/4 >0 \forall x`

`=> 6-2x=0`

`<=> 2x=6`

`<=> x=3`

Vậy `S={3}`

`6)`

`2(9x^2+6x+1)=(3x+1)(x-2)`

`<=> 2(3x+1)^2=(3x+1)(x-2)`

`<=> (6x+2)(3x+1)-(3x+1)(x-2)=0`

`<=> (3x+1)(6x+2-x+2)=0`

`<=> (3x+1)(5x+4)=0`

`<=> [(3x+1=0),(5x+4=0):}`

`<=> [(x=-1/3),(x=-4/5):}`

Vậy `S={-1/3;-4/5}`

`8)`

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

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

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

`<=> (x-1)(4x-3)=0`

`<=> [(x-1=0),(4x-3=0):}`

`<=> [(x=1),(x=3/4):}`

Vậy `S={1;3/4}`

$\left\{\begin{matrix}
\dfrac{1}{2}xy=54\\ 
x+y=21
\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}
x=21-y\\ 
\dfrac{1}{2}(21-y)y=54
\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}
x=21-y\\ 
\dfrac{21}{2}y-\dfrac{1}{2}y^{2}=54
\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}
x=21-y\\ 
\dfrac{-1}{2}y^{2}+\dfrac{21}{2}y-54=0(*)
\end{matrix}\right.$
Xét phương trình (*) ta có:
$\Delta =\left ( \dfrac{21}{2} \right )^{2}-4.\dfrac{-1}{2}.(-54)=\dfrac{9}{4}>0$
$\Rightarrow$ Phương trình (*) có hai nghiệm phhana biệt
$y_{1}=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-\dfrac{21}{2}+\sqrt{\dfrac{9}{4}}}{2.\dfrac{-1}{2}}=9$
$y_{2}=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-\dfrac{21}{2}-\sqrt{\dfrac{9}{4}}}{2.\dfrac{-1}{2}}=12$
\(\Rightarrow \left[ \begin{array}{l}x=21-9=12\\x=21-12=9\end{array} \right.\)