Question

$$( x + \frac { 1 } { 2 } ) ( x - \frac { 1 } { 2 } ) = x ^ { 2 } - \frac { 1 } { x ^ { 6 } }$$

Solve for x (complex solution)

$x\in -\sqrt[3]{2},\sqrt[3]{2}e^{\frac{\pi i}{3}},\sqrt[3]{2}e^{\frac{5\pi i}{3}},\sqrt[3]{2},\sqrt[3]{2}e^{\frac{2\pi i}{3}},\sqrt[3]{2}e^{\frac{4\pi i}{3}}$

Solve for x

$x=-\sqrt[3]{2}\approx -1.25992105$
$x=\sqrt[3]{2}\approx 1.25992105$