You are right to be puzzled! The formula Fe₃O₄ seems to contradict the usual valencies of iron (Fe²⁺ and Fe³⁺). Here's the explanation:

Fe₃O₄ is a mixed-valence compound. This means it contains iron atoms in more than one oxidation state. Specifically, it contains both Fe²⁺ and Fe³⁺ ions.

Here's how the formula works:

* Imagine the compound as a combination of two simpler oxides: FeO (ferrous oxide) and Fe₂O₃ (ferric oxide).

* The actual formula is a combination of these: FeO·Fe₂O₃. This represents one Fe²⁺ ion and two Fe³⁺ ions for a total of three iron atoms.

* Simplifying the formula: Combining the oxides gives Fe₃O₄.

In summary: The formula Fe₃O₄ represents a compound where iron exists in both +2 and +3 oxidation states. This allows the compound to be electrically neutral, despite the seemingly unusual combination of valencies.