The indeterminate form problem

Question

How to solve for $a$

$a\pm k$(k being any real number other $0$)=$\frac{a}{a}=a^2=a$ Find $a$ ( $k$ is any real number other than $0$

The only solution I could think of is $$\frac{0}{0}$$

But does it belong to real numbers and is my solution correct?

There is no real solution to $a\pm k = \frac aa=a=a^2, k\neq 0$ — Graham Kemp, May 26 '14 at 18:01
no, division by 0 isn't defined for reals numbers (to preserve their field structure) — Alessandro Codenotti, May 26 '14 at 18:02
@user153283 No, $\frac 00$ is undefined. Also, $0\pm k \neq 0, \text{ when } k\neq 0$. — Graham Kemp, May 26 '14 at 18:07
@user153283 If $k=0$ the solution would be $a=1$. Elsewhere there is no solution. — Graham Kemp, May 26 '14 at 18:11

score 2 · Answer 1 · answered May 26 '14 at 17:58

2

$$a \pm k = \ldots = a \implies a \pm k - a = 0 \implies \pm k = 0$$

answered May 26 '14 at 17:58

Karolis Juodelė

1 Answers1