is given with m and n real numbers and it's solutions.

It's asked for the value of the determinant:

I have tried to solve it in the Vandermonde way

Or to sum up columns 2 and 3 to the first (to obtain the sum, and the sum of squares of the solutions - which are found easily with Viete).

I have managed to find out that:

the value of the determinant beeing thinking that I should sqare the first identety and make some conection with this one.

I'm sorry for posting this problem to pre-algebra too. This is a linear algebra problem, but it's for highschool.