Question 129
Let $a,b,c,d$ be real numbers satisfying
$$(a+c)(b+d)=\sqrt2(ac-2bd-1).$$
Prove that
$$(ab-1)^2+(bc-1)^2+(cd-1)^2+(da-1)^2+(ac-1)^2+(2bd+1)^2\ge4.$$
$$(a+c)(b+d)=\sqrt2(ac-2bd-1).$$
Prove that
$$(ab-1)^2+(bc-1)^2+(cd-1)^2+(da-1)^2+(ac-1)^2+(2bd+1)^2\ge4.$$