Prove that x 2 + y2 - 1 is irreducible in q[ x, y].

Suppose that the polynomial x^2+y^2-1 is not irreducible. 
It means that there exists two fractions such that :

We found that q divide t and q divide s, but s and t are supposed to be prime each other. It is a contradiction. 
The polynomial x^2+y^2-1 is then irreducible in q[x,y] 

Ithink the answer is $2.10