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2022 SSMO Team Round Problems/Problem 9

Revision as of 12:06, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Given real numbers <math>a,b,x,y</math> 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 <...")
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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

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