Đáp án:
`a)` `S={-3;2}`
`b)` `S={-4;0;3;7}`
Giải thích các bước giải:
`a)` `x(x+1)(x-1)(x+2)=24`
`<=>[x(x+1)][(x-1)(x+2)]=24`
`<=>(x^2+x)(x^2+x-2)=24`
`text{đặt}` `x^2+x=a`
`<=>a(a-2)=24`
`<=>a^2-2a-24=0`
`<=>a^2+4a-6a-24=0`
`<=>a(a+4)-6(a+4)=0`
`<=>(a+4)(a-6)=0`
`<=>`$\left[\begin{matrix} a+4=0\\ a-6=0\end{matrix}\right.$
`<=>`$\left[\begin{matrix} a=-4\\ a=6`\end{matrix}\right.$
`text{TH1}` `a=-4`
`<=>x^2+x+4=0`
`<=>x^2+2*x*1/2+1/4+15/4=0`
`<=>(x+1/2)^2=-15/4`
`text{vì}` `(x+1/2)^2geq0`
`text{mà}` `(x+1/2)^2=-15/4`
`=>``text{ trên vô nghiệm}`
`text{TH2}` `a=6`
`<=>x^2+x-6=0`
`<=>x^2+3x-2x-6=0`
`<=>x(x+3)-2(x+3)=0`
`<=>(x+3)(x-2)=0`
`<=>`$\left[\begin{matrix} x+3=0\\ x-2=0\end{matrix}\right.$
`<=>`$\left[\begin{matrix} x=-3\\ x=2\end{matrix}\right.$
`text{vậy}` `S={-3;2}`
`---------------------`
`b)` `(x+2)(x+3)(x-5)(x-6)=180`
`<=>[(x+2)(x-5)][(x+3)(x-6)]=180`
`<=>(x^2-3x-10)(x^2-3x-18)=180`
`text{đặt}` `x^2-3x-10=b`
`<=>b(b-8)=180`
`<=>b^2+10b-18b-180=0`
`<=>b(b+10)-18(b+10)=0`
`<=>(b+10)(b-18)=0`
`<=>`$\left[\begin{matrix} a+10=0\\ b-18=0\end{matrix}\right.$
`<=>`$\left[\begin{matrix} b=-10\\ b=18`\end{matrix}\right.$
`text{TH1}` `b=-10`
`<=>x^2-3x-10=-10`
`<=>x^2-3x=0`
`<=>x(x-3)=0`
`<=>`$\left[\begin{matrix} x=0\\ x-3=0\end{matrix}\right.$
`<=>`$\left[\begin{matrix} x=0\\ x=3\end{matrix}\right.$
`text{TH2}` `b=18`
`<=>x^2-3x-10=18`
`<=>x^2-3x-28=0`
`<=>x^2+4x-7x-28=0`
`<=>x(x+4)-7(x+4)=0`
`<=>(x+4)(x-7)=0`
`<=>`$\left[\begin{matrix} x+4=0\\ x-7=0\end{matrix}\right.$
`<=>`$\left[\begin{matrix} x=-4\\ x=7\end{matrix}\right.$
`text{vậy}` `S={-4;0;3;7}`
`text{xin 5 sao và hay nhất nha}`
