Breakdown of Вам нужно использовать свой мозг, чтобы решить эту задачу.
вы
you (plural or formal)
этот
this [f: эта, n: это]
решить
to solve
задача
task
Questions & Answers about Вам нужно использовать свой мозг, чтобы решить эту задачу.
Why is it Вам нужно instead of Вы нужно?
The word нужно means "it is necessary." In Russian, the person who needs to do something is put in the Dative case. So, the sentence literally translates to "To you it is necessary to use..."
Why use свой for "your" brain instead of ваш?
Свой is a reflexive pronoun meaning "one's own," and it refers back to the person doing the action (in this case, the implied "you"). When you act upon your own body parts or belongings, Russian strongly prefers свой. Using ваш here would sound unnatural, as if you were using a brain that isn't currently in your head!
Since this lesson is about the У + Genitive construction for body parts, why don't we use У вас... here when talking about the brain?
The у вас болит (your ... hurts) construction is specifically for expressing involuntary states happening to your body, like pain. In this sentence, you are actively using the body part as a direct object to complete an action. Therefore, we treat мозг like a normal noun receiving an active verb (использовать) and modify it with a possessive pronoun (свой).
Why do we need чтобы here? Can't we just put the infinitive решить directly after the first clause?