prove that solution of min problem is unique

Hi

I have such exercise:

Let U be an open convex set of R^n and f be a strictly quasi-convex function.

Show that if there exists a solution of minimization problem, then it is a unique solution.

The problem Q is: min f(x) for all x belonging to U

I know that in 1dim f is strictly quasi-convex <=> for all (x,y)belonging to U^2, x not=y, for all t belonging to (0,1)

f(tx+(1-t)y) < max (f(x), f(y))

but here we have n-dimensional problem, so I am horribly confused and really don't know how to do this :/

Do you know how to solve it?