Question

Mathematics can uh solve this please ​

Answer 1

`a^3 + 1 = 0`

Explanation:

We start with the equation:

`a + (1)/(a) = 1`

We want to find the value of:

`a^3 + 1 =`

We can start with our previous equation and multiply both sides by a:

`(a + (1)/(a))*a = 1*a\\a^2 + 1 = a`

Now we can rewrite our initial expression as:

`a = 1 - (1)/(a)`

Replacing that in the right side, we get:

`a^2 + 1 = a = 1 - (1)/(a)`

Now again, let's multiply both sides by a

`a*(a^2 + 1) = a*(1 - (1)/(a) )\\a^3 + a = a - a/a\\a^3 + a = a - 1\\a^3 = -1\\a^3 + 1 = 0`

So we can conclude that:

`a^3 + 1 = 0`