1. \(\left(x+1\right)\left(x^2-x+1\right)-2x=x\left(x-1\right)\left(x+1\right)\)
\(\Rightarrow x^3+1-2x=x\left(x^2-1\right)\)
\(\Rightarrow x^3-x^3+x-2x=-1\)
\(\Rightarrow x=1\)
2. \(\left(x-2\right)^3+\left(3x-1\right)\left(3x+1\right)=\left(x+1\right)^3\)
\(\Rightarrow x^3-6x^2+12x-8+9x^2-1-x^3-3x^2-3x-1=0\)
\(\Rightarrow9x=9\)
\(\Rightarrow x=1\)
1) x3 + 1 - 2x = x3 - x
⇔ x3 + 1 - 2x - x3 + x = 0
⇔ 1 - x = 0 ⇔ x = 1
Vậy phương trình có nghiệm là x = 1.
2) ( x - 2 )3 + ( 3x -1 )( 3x + 1 ) = ( x + 1 )3
⇔ x3 - 6x2 + 12x - 8 + 9x2 - 1 = x3 + 3x2 + 3x + 1
⇔ x3 - 6x2 + 12x - 8 + 9x2 - 1 - x3 - 3x2 - 3x - 1 = 0
⇔ 9x - 10 = 0 ⇔ x = \(\dfrac{10}{9}\)
Vậy phương trình có nghiệm là x = \(\dfrac{10}{9}\)
