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So I get that 見つける takes an object and 見つかる doesn't, but can anyone tell me if
there are any major differences between 答えを見つけた and 答えが見つかった

If I came across an answer by chance, does the second sentence do a better job
at expressing that?

And also: 答えが見つけられた

What is different between sentence 2 and 3? (And aren't they both passive?)

Thank you :D And sorry if duplicate or dumb question
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nuances passive-voice transitivity
Nuances? 見つける vs 見つかる
I think you seem to notice that 見つける is a transitive verb and 見つかる is an
intransitive verb.

A subject is omitted in 答えを見つけた, for example、彼が答えを見つけた(He found the answer.).
On the other hand, 答え is a subject in 答えが見つかった.

答えが見つけられた(The answer was found) is passive form of 答えを見つけた and it has a nuance
like "by someone", but we don't use it often. Both 答えが見つけられた and 答えが見つかった seem
to be translated as "The answer was found".
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answer