Difference between revisions of "2022 SSMO Team Round Problems/Problem 9"
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==Problem== | ==Problem== | ||
| − | Given real numbers <math>a,b,x,y</math> such that | + | Given real numbers <math>a,b,x,y</math> such that |
| + | \begin{align*} | ||
| + | a^2+b^2&=1,\\ | ||
| + | x^2+y^2&=1,\text{and}\\ | ||
| + | abxy-\frac{1}{8}&=b^2y^2, | ||
| + | \end{align*} | ||
| + | find the sum of all distinct values of <math>(a+b+x+y)^2</math>. | ||
==Solution== | ==Solution== | ||
Latest revision as of 19:16, 2 May 2025
Problem
Given real numbers 
such that
\begin{align*}
a^2+b^2&=1,\\
x^2+y^2&=1,\text{and}\\
abxy-\frac{1}{8}&=b^2y^2,
\end{align*}
find the sum of all distinct values of 
.
