2022 SSMO Team Round Problems/Problem 9

Problem

Given real numbers $a,b,x,y$ such that <align*> a^2+b^2&=1,\ x^2+y^2&=1,\ abxy-\frac{1}{8}&=b^2y^2, </align*> find the sum of all distinct values of $(a+b+x+y)^2$.

Solution