\(\Leftrightarrow8x^9+2x^3=x^3+3x^2+3x+1+x+1\)
\(\Leftrightarrow8x^9+2x^3=\left(x+1\right)^3+\left(x+1\right)\)
Đặt $2x^3=a;x+1=b$ có:
\(a^3+a=b^3+b\)
\(\Leftrightarrow\left(a-b\right)\left(a^2+ab+b^2+1\right)=0\)
\(\Leftrightarrow a=b\left(doa^2+b^2+ab+1>0\right)\)
hay \(2x^3=x+1\)
\(\Leftrightarrow\left(x-1\right)\left(2x^2+2x+1\right)=0\)
\(\Leftrightarrow x=1\left(2x^2+2x+1=x^2+\left(x+1\right)^2>0\forall x\right)\)
Vậy $x=1$ t/m đề
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