"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).
What is the tense ot the sentence "The problem has been solved"
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...
As @JohnWaylandBales replied you also have intractable but you were asking for "cannot be solved" not "hard to solve". There is an interesting word for a problem so hard to solve within its (usually implied) rules but so important that someone breaks those rules in order to obtain a solution: a gordian knot problem, cutting the gordian knot.
Is there any idiom about the problems so bad that cannot be solved ...
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?
It's suitable for when the problem has been solved (there is, then, no problem to solve) and make-work is being done to create the solution where there is no problem. It's not so much implying that there is repetition of solution, though.
In context, I reported an online problem and in response the the service executive did her job but was not sure about whether hr action had solved the problem, so she asked me whether my problem was solved. In answer to that, could I correctly have said "the problem got solved"?