Đáp án:
x=0
Giải thích các bước giải:
\(
\begin{array}{l}
\sqrt[3]{{x - 1}} + \sqrt[3]{{x + 8}} = 1 + x^3 \\
\Leftrightarrow \sqrt[3]{{x - 1}} + 1 - 2 + \sqrt[3]{{x + 8}} = x^3 \\
\Leftrightarrow \frac{{x - 1 + 1}}{{\sqrt[3]{{(x - 1)^2 }} - \sqrt[3]{{x - 1}} + 1}} + \frac{{x + 8 - 8}}{{\sqrt[3]{{(x + 8)^2 }} + 2\sqrt[3]{{x + 8}} + 4}} = x^3 \\
\Leftrightarrow \frac{x}{{\sqrt[3]{{(x - 1)^2 }} - \sqrt[3]{{x - 1}} + 1}} + \frac{x}{{\sqrt[3]{{(x + 8)^2 }} + 2\sqrt[3]{{x + 8}} + 4}} - x^3 = 0 \\
\Leftrightarrow x(\frac{1}{{\sqrt[3]{{(x - 1)^2 }} - \sqrt[3]{{x - 1}} + 1}} + \frac{1}{{\sqrt[3]{{(x + 8)^2 }} + 2\sqrt[3]{{x + 8}} + 4}} - x^2 ) = 0 \\
\Leftrightarrow x = 0 \\
\end{array}
\)
