Question

Se
$\sqrt[3]{a } = 2$
então o valor da expressão
$- \sqrt[3]{ {a}^{2} } + \sqrt[3]{ \frac{1}{a} }$
é:

(A)
$\frac{ - 7}{2}$
(B)
$\frac{ - 5}{2}$
(C)
$- 1$
(D)
$\frac{1}{2}$
(E)
$\frac{7}{2}$

​

Answer 1

$-\sqrt[3]{a^2}~+~\sqrt[3]{\frac{1}{a}}~=\\\\\\=~-\left(\sqrt[3]{a}\,\right)^2~+~\dfrac{\sqrt[3]{1}}{\sqrt[3]{a}}\\\\\\=~-\left(2\right)^2~+~\frac{1}{2}\\\\\\=~-4~+~\frac{1}{2}\\\\\\=~\frac{2~.~(-4)~+~1~.~1}{2}\\\\\\=~\frac{-8+1}{2}\\\\\\=~\boxed{\frac{-7}{2}}$

Resposta: Letra A