Question

Giải pt: (x-1)(x²+x+1)-2x=x(x-1)(x+1)

Answer 1

\(\left(x-1\right)\left(x^2+x+1\right)-2x=x\left(x-1\right)\left(x+1\right)\)

\(\Leftrightarrow x^3-x^2+x+x^2-x+1-2x=x\left(x^2-1\right)\)

\(\Leftrightarrow x^3-2x+1-x^3+x=0\)

\(\Leftrightarrow-x=-1\Leftrightarrow x=1\)

Answer 2

Bài làm:

Ta có: \(\left(x-1\right)\left(x^2+x+1\right)-2x=x\left(x-1\right)\left(x+1\right)\)

\(\Leftrightarrow x^3-1-2x=x^3-x\)

\(\Leftrightarrow x=-1\)

Answer 3

( x - 1 )( x² + x + 1 ) - 2x = x( x - 1 )( x + 1 )

<=> x³ - 1 - 2x = x( x² - 1 )

<=> x³ - 1 - 2x = x³ - x

<=> x³ - 1 - 2x - x³ + x = 0

<=> -x - 1 = 0

<=> -x = 1

<=> x = -1

Vậy nghiệm của phương trình là x = -1

Answer 4

(x-1)(x²+x+1)–2x=x(x−1)(x+1)

⇔ x^3+1−2x=x(x^2−1)

⇔ x^3+1−2x=x^3−x

⇔ x^3−x^3−2x+x=−1

⇔ −x=−1

⇔ x=1

Answer 5

\(\left(x-1\right)\left(x^2+x+1\right)-2x=x\left(x-1\right)\left(x+1\right)\)

\(\Leftrightarrow x^3+x^2+x-x^2-x-1=x\left(x^2+x-x-1\right)\)

\(\Leftrightarrow x^3-1=x^3-x\)

\(\Leftrightarrow x^3-1-x^3+x=0\Leftrightarrow-1+x=0\)

\(\Leftrightarrow x=1\)