Four real numbers
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
,
![q](/media/m/c/1/d/c1db9b1124cc69b01f9a33595637de69.png)
,
![r](/media/m/3/d/f/3df7cc5bbfb7b3948b16db0d40571068.png)
,
![s](/media/m/9/0/8/908014cbadb69e42261a56b450a375b9.png)
satisfy
![p+q+r+s = 9](/media/m/2/8/6/286f97e39bad93c780a93f8d96f169d3.png)
and
![p^{2}+q^{2}+r^{2}+s^{2}= 21](/media/m/a/9/3/a93e353b635a176700e92d4cc150d771.png)
. Prove that there exists a permutation
![\left(a,b,c,d\right)](/media/m/5/d/c/5dcbfa525e6480a23e58107ea1d53ca3.png)
of
![\left(p,q,r,s\right)](/media/m/e/8/b/e8b82015a9dc408668b36f8c57d82c99.png)
such that
![ab-cd \geq 2](/media/m/4/8/6/48627f5898b390e92bde6eec3fa07d0b.png)
.
%V0
Four real numbers $p$, $q$, $r$, $s$ satisfy $p+q+r+s = 9$ and $p^{2}+q^{2}+r^{2}+s^{2}= 21$. Prove that there exists a permutation $\left(a,b,c,d\right)$ of $\left(p,q,r,s\right)$ such that $ab-cd \geq 2$.