+0  
 
0
1
1
avatar+713 

Evaluate $a^3 - \dfrac{1}{a^3}$ if $a - \dfrac{1}{a} = 0$.

 Jul 10, 2024
 #1
avatar+1256 
+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! :)

 Jul 10, 2024

2 Online Users

avatar
avatar