Question 3
Four real numbers $p,q,r,s$ satisfy
$$ p+q+r+s=9\quad\text{and}\quad p^{2}+q^{2}+r^{2}+s^{2}=21. $$
Prove that $ab - cd \geq 2$ holds for some permutation $(a,b,c,d)$ of $(p,q,r,s)$.
$$ p+q+r+s=9\quad\text{and}\quad p^{2}+q^{2}+r^{2}+s^{2}=21. $$
Prove that $ab - cd \geq 2$ holds for some permutation $(a,b,c,d)$ of $(p,q,r,s)$.