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MathNet 2012 Question 95

Math Olympiad Vault · MathNet 2012

Question 95

Non-zero real numbers $a$, $b$, $c$, $d$ satisfy the equalities
$$
a + b + c + d = 0, \quad \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} + \frac{1}{abcd} = 0.
$$
Find all possible values of the product $(ab - cd)(c + d)$.