Assalaamu Alikum Wa Rahmatullahi Wa Barakaatuh
Bismellah wa Tawakkalna ala Allah
before starting and first of all I want ya to know that; I am not knowledgeable person, I have not this kind of knowledge, and most of my posts to you are results of some reseaches I do not because I have any kind of any knowledge.... when you ask something, I search to learn to benefit you so, we are learning ^-^ I am no better than anyone, understood?...ok Alhamdulilah now the word Yaku.
The Word يَكُ :
The origin of the word( يَكُ yaku) is the word (يكون yakoon) which means: Be. But what happened and changed it?
Let's return to the Aayah you have posted above and which is:
فَلَمْ يَكُ يَنفَعُهُمْ إِيمَانُهُمْ لَمَّا رَأَوْا بَأْسَنَا سُنَّتَ اللَّـهِ الَّتِي قَدْ خَلَتْ فِي عِبَادِهِ وَخَسِرَ هُنَالِكَ الْكَافِرُونَ
In the Aayah it came ( لَمْ ) before the verb, but what about لَمْ
لَمْ lam:is a negtive particle which turns the verb (only the imperfective verb) in the Jussive mood or case.
* It came before the imperfective verb ( يَكُوْن ) and turned it in the Jussive mood; giving its final letter the Sukoon harakat. And for that; the verb ( يَكُوْنْ ) had two still letters which are ( ن and و ).
* So, to prevent two still letters from directly following each other; we omitted the letter ( و ) and for this the word became ( يَكُنْ ).
* Then we omitted the letter ( ن ) for Takh'feef ("reduction" to ease the pronunciation of the word) and then it became ( يَكُ ).
P.S.
the omission of the Noon here is not waajib so, we can omit it if we want and we can just keep it, still both are right in this case of E'eraab.
now we know Yaku's general meaning, origin and the reason why it changed form its origin to what it is now , please if anyone see anything wrong with what I have posted then correct me and teach us all the right answers ...
love ya all for Allah's sake.
i was confused that i might be wrong if sister shadin is so much confident in it. 
