VTMO 2026 - Grade 8 - Final - SET 1 - Self-study Question 5

Let $a,b,c,d$ be real numbers satisfying $(a+b)(c+d)=2$, $(a+c)(b+d)=3$ and $(a+d)(b+c)=4$. Find the minimum value of $a^2+b^2+c^2+d^2$.