Which one of those two sentences is correct?
Do you not think it has made our lives better ?
Do not you think it has made our lives better ?
I want to know if the technology has made our lives better or not.
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The basic declarative word order looks like this:
- You do not think it has made our lives better.
We can turn this into a question by inverting the subject you with the auxiliary do:
- Do you not think it has made our lives better?
But not doesn't move before the subject. It's a separate word and is unaffected by subject–auxiliary inversion.
We can also take example 1 and contract do not to don't:
- You don't think it has made our lives better.
Now we can form a question by inverting the subject you with the negated auxiliary don't:
- Don't you think it has made our lives better?
In this case, -n't moves along with do. The contracted form is a single word.
There's no grammar that results in Do not you think, so that word order is ungrammatical. You can't "uncontract" don't in example 4. Don't make the mistake of thinking you can replace don't with the uncontracted do not. That's not how English question formation works.
Do you not think it has made our lives better?
Don't you think it has made our lives better? It's incorrect to say "*Do not you...?"
These sentences are negative questions. The former is uncontracted, which is formed by beginning the sentence with "auxiliary + subject + not", whereas the latter is contracted, which begins with "auxiliary + n't + subject". Both the types are grammatically correct. The only difference is that the former is formal. On the other hand, the latter is more usual and used in formal and informal English.
Khan is correct as to the grammaticality. But I notice that you said you "wonder". So you really need to phrase the qestion positively: "DO you think..." this is because if you use negative query, it is taken to mean an assertion to be accepted or opposed, like "I think so, don't you think so too?" Oddly enough, the negative query is a way to encourage a positive response.