Hi, need a bit of help with this question.

The curve $\displaystyle y = -x + \tanh{48x}$, $\displaystyle x \ge 0$ has a maximum turning point at A, find the x co-ordinates of A in exact logarithmic form.

Differentiated the equation to get$\displaystyle x = \frac{ln{(7 \pm 4\sqrt{3})}}{49}$, which turns out to be right.

In the answers though, they only have $\displaystyle x = \frac{ln{(7 + 4\sqrt{3})}}{49}$, at first I though this was because you cannot take a natural log of a minus number, but $\displaystyle 7 - 4\sqrt{3}$ is a positive number.

Any ideas?

Thanks in advance.