For 3.21, I calculated the determinant,
\( \Delta = (2(m+1))^2 - 4*1*(3m^2+4mn+4n^2+1) = 2m^2-2m+4mn+4n^2+1 \geq 0
I simplified to \( (m-1)^2+(m+2n)^2 \geq 0 \)
but I don't know where to go from there since that doesn't tell you anything.
Are you sure your discriminant is simplified correctly? You canceled a negative number, and that reverses the direction of the inequality.