`a)x^4-5x^2+4=0`
`⇔x^4-4x^2-x^2+4=0`
`⇔x^2(x^2-4)-(x^2-4)=0`
`⇔(x^2-4)(x^2-1)=0`
`1)x^2-4=0⇔x^2=4⇔x=+-2`
`2)x^2-1=0⇔x^2=1⇔x=+-1`
Vậy `S={+-2;+-1}`
`b)(x^2+5x)^2-2(x^2+5x)=24`
`⇔(x^2+5x)^2-2(x^2+5x)-24=0`
Đặt `t=x^2+5x`
`t^2-2t-24=0`
`⇔t^2-6t+4t-24=0`
`⇔t(t-6)+4(t-6)=0`
`⇔(t-6)(t+4)=0`
`⇔(x^2+5x-6)(x^2+5x+4)=0`
`⇔(x-1)(x+6)(x+4)(x+1)=0`
`1)x-1=0⇔x=1`
`2)x+6=0⇔x=-6`
`3)x+4=0⇔x=-4`
`4)x+1=0⇔x=-1`
Vậy `S={+-1;-4;-6}`
`c)x(x+1)(x-1)(x+2)=24`
`⇔x(x+1)(x-1)(x+2)-24=0`
`⇔[x(x+1)][(x-1)(x+2)]-24=0`
`⇔(x^2+x)(x^2+x-2)-24=0`
Đặt `x^2+x=t`
`t.(t-2)-24=0`
`⇔t^2-2t-24=0`
`⇔t^2-6t+4t-24=0`
`⇔t(t-6)+4(t-6)=0`
`⇔(t-6)(t+4)=0`
`⇔`\(\left[ \begin{array}{l}t-6=0\\t+4=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x^2+x-6=0\\x^2+x+4=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}\left[ \begin{array}{l}x=-3\\x=2\end{array} \right.\\x^2+x=-4(vô nghiệm)\end{array} \right.\)
Vậy `S={-3;2}`
`d)x^4+2x^3+5x^2+4x-12=0`
`⇔x^4-x^3+3x^3-3x^2+8x^2+12x-8x-12=0`
`⇔(x^4-x^3)+(3x^3-3x^2)+(8x^2-8x)+(12x-12)=0`
`⇔x^3(x-1)+3x^2(x-1)+8x(x-1)+12(x-1)=0`
`⇔(x-1)(x^3+3x^2+8x+12)=0`
`⇔(x-1)(x^3+2x^2+x^2+2x+6x+12)=0`
`⇔(x-1)[(x^3+2x^2)+(x^2+2x)+(6x+12)]=0`
`⇔(x-1)[x^2(x+2)+x(x+2)+6(x+2)]=0`
`⇔(x-1)(x+2)(x^2+x+6)=0`
`1)x-1=0⇔x=1`
`2)x+2=0⇔x=-2`
`3)x^2+x+6=0⇔x^2+x=-6`(vô nghiệm)
Vậy `S={1;-2}`
