MathDB

What is the smallest value of

k

for which the inequality \begin{align*} ad-bc+yz&-xt+(a+c)(y+t)-(b+d)(x+z)\leq \\ &\leq k\left(\sqrt{a^2+b^2}+\sqrt{c^2+d^2}+\sqrt{x^2+y^2}+\sqrt{z^2+t^2}\right)^2 \end{align*} holds for any

8

real numbers

a,b,c,d,x,y,z,t

?
Edit: Fixed a mistake! Thanks @below.

Problem Statement