Matematické Fórum

Skrytý text:
Consider polynomials




Obviously are roots of and are roots of .

At first, the following identity holds:



But and since and also and since . Also , , so it must holds and , so , and therefore .

Skrytý text:

a,b,c are roots of
x,y,z are roots of
so taking difference of the two when t is some of the nonzero roots gives , so q1=q2, so both polynomials are equal and so have the same roots.
From the inequalities in supposition it then easilly follows a=x,b=y,c=z.

Edit: Wrong solution... no proof that t is the same in both equalities is given.