1, x²=$x^{5}$
⇔x²- $x^{5}$ =0
⇔x².(1-x³)=0
⇔x²=0 hay ⇔1-x³=0
⇔x=0 ⇔x³=1
⇔x=1
Vậy S={0;1}
2, 4x.(x+1)=8.(x+1)
⇔ 4x.(x+1)-8.(x+1)=0
⇔(4x-8)(x+1)=0
⇔4x-8=0 hay ⇔x+1=0
⇔4x=8 ⇔x=-1
⇔x=2
Vậy S={-1;2}
3, x. (x - 1) -2 . (1-x) =0
⇔ x. (x - 1) +2 . (x-1) =0
⇔(x+2)(x-1)=0
⇔x+2=0 hay ⇔x-1=0
⇔x=-2 ⇔x=1
Vậy S= { -2; 1}
4, 2x ( x-2) - ( 2 - x )^ 2 = 0
⇔2x²-4x-4+4x-x²=0
⇔x²-4=0
⇔(x-2)(x+2)=0
⇔x-2=0 hay ⇔x+2=0
⇔x=2 ⇔x=-2
Vậy S= {-2; 2}
5, ( x-3)^3 +3 -x =0
⇔ ( x-3)^3 -(x-3) =0
⇔[(x-3)²-1](x-3)=0
⇔[(x-3)²-1](x-3)=0
⇔(x-3-1)(x-3+1)(x-3)=0
⇔x-3=0 hay ⇔x-4=0 hay ⇔x-2=0
⇔x=3 ⇔x=4 ⇔x=2
Vậy S={ 2;3;4}
6, 5x.(x-2) - ( 2-x ) =0
⇔ 5x.(x-2) +( x-2 ) =0
⇔(5x+1)(x-2)=0
⇔5x+1=0 hay ⇔x-2=0
⇔5x=-1 ⇔x=2
⇔x=$\frac{-1}{5}$
Vậy S={ $\frac{-1}{5}$ ; 2}
