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Is either of the following correct?

X is known difficult to implement.
X is known to be difficult to implement.

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2 Answers

The only one of your choices that is a complete sentence is this:

X is known to be difficult to implement.

And there are verbs which fit the other structure, such as find, with which the to be is unnecessary:

X has been found [to be] difficult to implement.

Know with that usage, when it has ever occurred, has been archaic (He knew the climb dangerous).

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Searching Google books, it appears that the incorrect usage may not even be archaic; it appears to be used mainly by writers of technical papers with Chinese, Japanese, or Korean names. –  Peter Shor Mar 24 '12 at 11:10
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The first expression is possible with difficult to implement as an adjective, that is, a noun follows it:

X is a known difficult to implement plan.

Note, however, the added article a. It is also better to hyphenate the phrase (difficult-to-implement) or find a one-word substitute, except where the phrase is a recognized or defined term, such as in a particular field or within a particular document.

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