Let be the number such that . Find all that satisfy the given equations.
- We are given . From the formula for this means
Then, from the given equation we have
So, then we have
Therefore we have
- There can be no which satisfy the given equation. As in part (a), we use the definition of to obtain the equation,
Next, we use the equation given in the problem to write,
Furthermore, we can obtain an expression for by considering
Putting these expressions for and into our original equation we have
But this implies
which is impossible. Hence, there can be no real satisfying this equation.