Question

Giải phương trình :

( 2x² - 2x - 1 )³ + ( 2x - 1 )³ = ( x² - x + 1 )³ + ( x² + x - 3 )³

Giúp tớ với T.T

Answer 1

Cứ giả vờ.

Answer 2

bó tay! =_=

Answer 3

") hỏi thầy đi

Answer 4

Ta có: \(\left(2x^2-2x-1\right)^3+\left(2x-1\right)^3=\left(x^2-x+1\right)^3+\left(x^2+x-3\right)^3\)

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

\(2x^2-2x-1=a;2x-1=b;x-x^2-1=c\)

\(\Leftrightarrow a+b=2x^2-2;b+c=3x-x^2-2;c+a=x^2-x-2;a+b+c=x^2+x+3\)

\(\Leftrightarrow a^3+b^3+c^3=\left(a+b+c\right)^3\)

\(\Rightarrow3\left(a+b\right)\left(b+c\right)\left(c+a\right)=0\)

\(\Rightarrow a+b=0;b+c=0;c+a=0\Rightarrow2x^2-2=0;3x-x^2-2=0\Rightarrow x\in\left\{-1;1;2\right\};x^2-x=0\)