11.2. Find all quadruples of real numbers $(a, b, c, d)$ such that $a(b+c)=b(c+d)=c(d+a)=d(a+b)$.
Answer. 8 infinite series of solutions, obtained by multiplying each of the numbers $(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1),(1,1,1,1),(1,-1,1,-1),(1,-1 \pm \sqrt{2},-1,1 \mp \sqrt{2})$ by any real number.

Solution. Subtracting the first expression from the third, we get $a b=c d$, subtracting the fourth expression from the second, we get $a d=b c$.