"The problem has been solved" is the present perfect tense in the passive voice (it has been solved by someone). In "The problem is solved", "solved" is an adjective describing a state in the present tense. I don't understand your question 2).
The context is solving a mathematical problem. solved with sth - means a problem is tackled using sth method solved for sth - means that a problem is transformed in such way that can sth can be obtained directly (as in "solve for x") My question is, am I missing any meanings, or confusing them?
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What is the tense ot the sentence "The problem has been solved"
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Is resolved vs has been resolved? - English Language & Usage Stack Exchange
In a technical environment, what is the most suitable sentence to use when answering to someone about a problem that they had and we solved it for them: The problem is solved The problem has been s...