1. Eu preciso um amigo.
2. Eu preciso de um amigo.

Are both correct? If not, why?

Veja uma tradução

💨 Short answer:

【✔️】 “Eu 𝗽𝗿𝗲𝗰𝗶𝘀𝗼 𝗱𝗲 um amigo.”
【✖️】 “Eu 𝗽𝗿𝗲𝗰𝗶𝘀𝗼 um amigo.”

The preposition "de" is mandatory after "precisar" in this sentence because the object «um amigo» is a noun phrase.

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📚️ Detailed Explanation:

① «Precisar de» will always go with a noun, a pronoun, or a noun phrase.

💬𝘗𝘳𝘦𝘤𝘪𝘴𝘢𝘳 𝘥𝘦 + [𝘯𝘰𝘶𝘯]
— “Eu preciso de [ajuda].”
⤷ “I need [help].”

💬𝘗𝘳𝘦𝘤𝘪𝘴𝘢𝘳 𝘥𝘦 + [𝘱𝘳𝘰𝘯𝘰𝘶𝘯]
— “Eu preciso de [alguém].”
⤷ “I need [someone].”

💬𝘗𝘳𝘦𝘤𝘪𝘴𝘢𝘳 𝘥𝘦 + [𝘯𝘰𝘶𝘯 𝘱𝘩𝘳𝘢𝘴𝘦]
— “Eu preciso de [uma faca afiada].”
⤷ “I need [a sharp knife].”

② «Precisar» without a preposition can be either used intransitively or followed by another verb/clause.

💬𝘗𝘳𝘦𝘤𝘪𝘴𝘢𝘳 - 𝘐𝘯𝘵𝘳𝘢𝘯𝘴𝘪𝘵𝘪𝘷𝘦 𝘶𝘴𝘢𝘨𝘦
— “Eu preciso, obrigada.”
⤷ “I need it, thank you.”

💬𝘗𝘳𝘦𝘤𝘪𝘴𝘢𝘳 + [𝘷𝘦𝘳𝘣]
— “Eu preciso [estudar].”
⤷ “I need [to study].”

💬𝘗𝘳𝘦𝘤𝘪𝘴𝘢𝘳 + [𝘤𝘰𝘰𝘳𝘥𝘪𝘯𝘢𝘵𝘦 𝘤𝘭𝘢𝘶𝘴𝘦]
— “Eu preciso [que ele chegue].”
⤷ “I need [him to arrive].”