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The phrase "approaches have failed" is correct and usable in written English.
You can use it when discussing methods or strategies that did not achieve their intended outcomes.
Example: "Despite numerous attempts to solve the issue, all approaches have failed to yield positive results."
Alternatives: "methods have not succeeded" or "strategies have proven ineffective."
Exact(51)
Often, though, these approaches have failed.
More complex approaches have failed to produce consistent results.
Glover considers it unethical to ignore G.M. crops if other approaches have failed.
"A future where we embrace the possibility of new solutions to enduring problems where old approaches have failed.
Conventional approaches have failed to respond to the needs of the community without this involvement in decision making.
Despite decades of work, various bottoms-up, synthetic biomaterials approaches have failed to produce a functional construct suitable for transplantation.
Similar(9)
In one study, all thirty-four recipients were cured; these are people for whom all other approaches had failed.
Mr Ainsworth, a Home Office minister under Tony Blair, said successive governments' approaches had failed, leaving criminal gangs in control.
The patients were selected because traditional clinical molecular genetic approaches had failed to uncover the causal mutation.
However, most previous studies using a partial adjustment approach have failed to recognize the possibility of an endogenous lagged dependent variable in the regressors (Hosoe and Akiyama 2009).
Nonetheless, decades of research with this approach have failed to explain all aspects of human speech perception.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com