Question 34
Real numbers $a, b, c, d$ are such that
$$
a + b + c + d = 0 \quad \text{and} \quad \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} = 0.
$$
How many of the equalities
$$ab = cd, \quad ac = bd, \quad ad = bc$$
can hold simultaneously?
$$
a + b + c + d = 0 \quad \text{and} \quad \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} = 0.
$$
How many of the equalities
$$ab = cd, \quad ac = bd, \quad ad = bc$$
can hold simultaneously?