# equation solving – Solve misses positive solutions

Why `Solve` returns only negative solutions?

``````Solve((x + 1)^(2 n) + (x - 1)^(2 n) == 0, x)
``````

$$left{left{xto frac{1+e^{frac{i pi }{2 n}}}{-1+e^{frac{i pi }{2 n}}}right}right}$$

But we know conjugates are also a solution i.e.

$$left{left{xto -frac{1+e^{frac{i pi }{2 n}}}{-1+e^{frac{i pi }{2 n}}}right}right}$$

are also solutions.

We see that

``````With({n = 1}, Solve((x + 1)^(2 n) + (x - 1)^(2 n) == 0, x))
``````

returns

$${{xto -i},{xto i}}$$

and
$$left{left{xto frac{1+e^{frac{i pi }{2 n}}}{-1+e^{frac{i pi }{2 n}}}right}right} /. n -> 1$$

returns

$$i$$