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MathNet 2014 Question 7

Math Olympiad Vault · MathNet 2014

Question 7

Given positive real numbers $a, b, c, d$ that satisfy equalities
$$
a^2 + d^2 - ad = b^2 + c^2 + bc \quad \text{and} \quad a^2 + b^2 = c^2 + d^2,
$$
find all possible values of the expression $\frac{ab+cd}{ad+bc}$.