# Solve contains wrong solution

Hello, I tried to following to find a maxima of a function:

```
var('t x');
f=(e^(x*t))*(x-1)^2;
maxima = solve([derivative(f,x)==0, derivative(f,x,2)<0],x)
show(maxima);
```

And the solution sage spits out are:

```
[
[x == 1, -2 > 0],
[x == (t - 2)/t, -(t - 2)^2 + 2*(t - 2)*t - t^2 + 6 > 0]
]
```

I understand that sage cannot evaluate the validity of the second solution but the first one surely is no solution at all.

Why does it give me this solution or am I doing anything wrong?

I know, that I could only solve for f'(x)==0 and filter for f''(x)<0 but solve shouldn't contain solutions like that, I think.