resposta:
Resolução:
$\,a\,+\,\dfrac{1}{a}\,=\,3\;\Rightarrow$ $\,(a\,+\,\dfrac{1}{a})^3\,=\,3^3\;\Leftrightarrow$ $\,a^3\,+\,3a\,+\,\dfrac{3}{a}\,+\,\dfrac{1}{a^3}\,=\,27\;\Leftrightarrow$ $\,a^3\,+\,\dfrac{1}{a^3}\,+\,3a\,+\,\dfrac{3}{a}\,=\,27\;\Leftrightarrow$ $\,a^3\,+\,\dfrac{1}{a^3}\,+\,3(a\,+\,\dfrac{1}{a})\,=\,27\;\Leftrightarrow$ $\,a^3\,+\,\dfrac{1}{a^3}\,+\,3\,\centerdot \,3\,=\,27\;\Leftrightarrow$ $\,a^3\,+\,\dfrac{1}{a^3}\,=\,27\,-\,9\,=\,18\,$
×