#1**+1 **

first, let's focus in the equation we are given.

Squaring both sides of the equation, we get that

\((a^2 + 2 + 1/a^2) = 0\)

This means that we have \(a^2 + 1/a^2 = -2\)

Now, let's focus on what we are trying to find.

Let's notice that

\(a^3 - 1/a^3 = ( a - 1/a) ( a^2 + 1 + 1/a^2) \)

Wait a minute! we already have all the terms needed. We know both values to solve the problem.

Since the first term is 0, we just have \((0)(-1) = 0\)

So 0 is our answer.

Thanks! :)

NotThatSmart Jul 10, 2024