三道初一解方程

1.
x^3+1-2x^2-2x=0.
<=>(x+1)(x^2-x+1)-2x(x+1)=0
<=>(x+1)(x^2-x+1-2x)=0
<=>(x+1)(x^2-3x+1)=0
<=>(x+1)[((x^2-2*3/2*x+9/4)-5/4]=0
<=>(x+1)[(x-3/2)^2-5/4]=0
=>x+1=0或x-3/2=√5/2或x-3/2=-√5/2.
<=>x=-1或x=(3+√5)/2或x=(3-√5)/2.

2.
(X②-5X+1)(X②-5X+9)+15=0
假令t=x^2-5x.
=>(t+1)(t+9)+15=0
<=>t^2+10t+24=0
<=>(t+4)(t+6)=0
=>t=-4或t=-6.
即：x^2-5x+4=0或x^2-5x+6=0
=>(x-4)(x-1)=0或(x-2)(x-3)=0.
=>x=1或x=2或x=3或x=4.

3.
.(X②+2)②+8X(X②+2)+15X②=0
假令x^2+2=t.
=>t^2+8x+15x^2=0
<=>(t+3x)(t+5x)=0
=>t=-3x或t=-5x.
即：x^2+2+3x=0或x^2+5x+2=0.
=>(x+1)(x+2)=0或x^2+2*5/2*x+25/4-17/4=0.
<=>x=-1或x=-2或(x+5/2)^2=17/4.
=>x=-(5+√17)/2或x=-2或x=-1或x=(√17-5)/2.

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