Breakdown of Он смог решить задачу.
он
he / it (for a masculine noun) / it (for a neuter noun)
решить
to solve
задача
task
смочь
to manage to, to be able to (perfective)
Questions & Answers about Он смог решить задачу.
Why is the perfective verb решить used here instead of the imperfective решать?
The perfective решить is used because the focus is on the result of the action: successfully finishing the problem. If the sentence used the imperfective решать, it would mean he was able to work on or spend time on the problem, without necessarily getting the final answer.
Why use the perfective past tense смог instead of the imperfective мог?
The perfective смог translates well to "managed to" or "succeeded in". It tells us he actually achieved the action in a specific, successful instance. The imperfective мог would just mean he "had the ability" or "could" do it in a general sense, without confirming he actually did it this time.
Doesn't решить usually mean "to decide"?
Yes, решить is a very common verb for "to decide". However, when you pair it with a word like задача (a task, exercise, or math problem) or проблема (problem), the meaning naturally becomes "to solve".
Why does the word for "problem" end in -у (задачу) instead of -а?
Because it is the direct object of the verb решить (the thing being solved), it must take the accusative case. The dictionary form is the feminine noun задача, and for feminine nouns ending in -а, the ending changes to -у in the accusative case.