还 in 你还好吗 has the meaning of "still" , "as well", "even", or just for "emphasis (强调)" and no meaning here?
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你好吗? = how are you?
你(还好)吗? = are you (still ok)?
You need the 还 in 你还好吗 to indicate you are still alright. (nothing bad has happened)
For example, if someone slipped and fell, his friend wouldn't ask him 你好吗? (how are you). His friend would ask 你还好吗? (are you still ok)
If you ask a friend 最近生意如何? (How's business?), the typical reply would be
非常好 (extremely good/ very good)
很好 (very good/ good)
还好 (good/ still good = still considered good = modestly good)
You can see '还' in '还好' indicates 'still' or 'modestly'