I have a Facebook page who has got few likes & that’s why not got display in Google search result .should I post the back links for Facebook page.
Does it increase the search visibility.
You joined Facebook only 3 days ago.
Do you know if Facebook pings Google or submits a revised sitemap every time a new page is created? I doubt that it does.
IMHO you just need to have a little more patience. In the meanwhile, keep posting new content to the page. Eventually Google will catch up.
posting good content and getting more likes for your Page, will improve your page in search results, posting backlinks will also help only if you have good content
Facebook page is for brand awareness and social media exposure, mostly people use it for back-links but no one can generate back links for the Facebook page, nice alternative you can do and see the difference & share with us. And when it comes to Facebook Page, Google also caches it, please be sure “Page” not “Wall”. So post even more, like other pages same as your niche, share with them, invite and allow them to share post on your page. All these helps you to optimize your Facebook page and you see a good difference.
Hello friend, to increase visibility only like would not work. For increasing visibility you should like more pages,you have to promote your facebook page on other social media sites. Also you can organize contest on facebook page. More people will visit your site then search visibility will increase. Fresh and new content you can post on your facebook page to attract traffic. Facebook is very good site to gain organic traffic and increase visibility.
If you want to increase the visibility so you have to post attractive and useful content regularly. When other user find useful content so you have automatically increase the visibility and real likes from others. You have to reach at other people who can be interested in your business by following them.
Social Media is the best way to convey your message to many people.
no backlinks has no relation with Facebook page like. and you don’t get any backlinks from people liking your page on Facebook.
You should understand that Facebook users like page when they find there something useful or interesting for them. It is the basic rule of like. So you should work on it. Your facebook page should be packed with something useful for other users so that they feel happy to visit that page again and again.
According to my perception backlinks not beneficial for your Facebook account backing just creating traffic and return you better Google Page rank. 
This topic ended in March, closing.