Question

Mathematics can uh solve this please ​

Answer 1

Answer:

$a^3 + 1 = 0$

Step-by-step explanation:

We start with the equation:

$a + \frac{1}{a} = 1$

We want to find the value of:

$a^3 + 1 =$

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

$(a + \frac{1}{a})*a = 1*a\\a^2 + 1 = a$

Now we can rewrite our initial expression as:

$a = 1 - \frac{1}{a}$

Replacing that in the right side, we get:

$a^2 + 1 = a = 1 - \frac{1}{a}$

Now again, let's multiply both sides by a

$a*(a^2 + 1) = a*(1 - \frac{1}{a} )\\a^3 + a = a - a/a\\a^3 + a = a - 1\\a^3 = -1\\a^3 + 1 = 0$

So we can conclude that:

$a^3 + 1 = 0$