Hi, let me join in.

I wonder if one of you can confirm that it's impossible to use this inspiron 7720 in a triple monitor setup (no duplicating but only extending the screen)? I wonder because it is usually possible with optimus cards and win7/8 but not this time - could only manage to run any 2 out of three.

And to answer riscy00: why use a splitter? Simply use HDMI and vga and disable the laptop screen. I did this today.

I know the OP raised the question about connecting two(2) external monitors as well as others asking about 3 monitors so here's some information regarding the questions.

Technically the 17R SE 7720 itself will allow up to 3 monitors (Built-in Display and 2 External Displays) to be connected in either Clone or Extended Mode and working all at once. Please see my reference section below for all the links that you'll need to understand this better and most of all how to hook it up.

@Albertsmtg The Nvidia GT 650M is a discrete GPU it has no display port logic it can only Render Graphics, it requires the Intel HD 4000 to actually display the rendered graphics to the attached displays, technically the Nvidia GT 650M can support up to 4 Active Displays but it's limited to what the Intel HD 4000 supports, see my reference section below.

Based on my Research:

The 17R SE 7720 is equipped with the following display ports (not to be mistaken for the trademark DisplayPorts physical port Technology)
1 External VGA Port, 1 External HDMI Port, 1 Built-in LCD Monitor connected via an LVDS interface (verified on my 17R SE 7720)

Without using Intel's WiDi technology (Drivers are available for the 17R SE 7720 in the Dell Driver Download Section) you'll be limited to using only 2 displays.

If you where looking to connect 2 external monitors with one on the HDMI port and another on the VGA port and get it to work this way (Option 2 in the table below), you will find that you are limited based on Intel's Configuration FAQ because the Built-in Display would have needed to been connected to an eDP interface, unfortunately the 17R SE 7720 uses an LVDS interface to accomplish this.  Option 1 in the table below may have been viable in this situation since the built-in display in this option may be connected via an LVDS interface but the 17R SE 7720 has no physical DisplayPort (trademark technology) ports.

So...
Using the Intel Configuration FAQ in my Reference section below and the 17R SE 7720's limitations of the unit having NO DisplayPorts along with the Built-in display being connected via an LVDS(Low-voltage differential signaling) interface instead of an eDP (embedded DisplayPort) interface you will need to use the 3rd configuration to get it to work properly.

Viable Connections from the Intel Configuration FAQ Table:

Active Display 1	Active Display 2	Active Display 3
DisplayPort*	DisplayPort	HDMI* or DVI or VGA or DisplayPort or Built-in Display2
DisplayPort or HDMI or DVI or VGA	DisplayPort or HDMI or DVI or VGA	Built-in Display3
DisplayPort or HDMI or DVI or VGA or Built-in Display2	DisplayPort or HDMI or DVI or VGA	Intel® Wireless Display (Intel® WiDi)

1 To check if your computer's built-in display uses an embedded DisplayPort (eDP) or LVDS connector type:
From the Windows* desktop press Ctrl+Alt+F12 (My note here, this works if you have the Hotkey sequence enabled in the Intel Graphics and Media Control Center) key combination. If prompted select Advanced Mode application mode. Select Options and Support, Select Information Center, Change the System Information drop down to Built-in Display. Check the Connector Type field.

2 Built-in display uses connector types: eDP off the chipset or LVDS.

3 Built-in display uses eDP off a mobile processor.

 

 

Cheers
Hope the information helps everyone.

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References -

Link: Intel HD 4000 Technical Specification write up:

Summary - "Another new feature is the support for up to 3 independent displays (depends on how the HD 4000 is used in the laptop - maybe only with a DisplayPort / eDP) as AMD offers with theirs Eyefinity support (up to 6 displays)."

Link: Nvidia GT 650M Technical Specification write up:

Summary - "The improved feature set now includes support for up to 4 active displays. Furthermore, high resolution monitors of up to 3840x2160 pixels can now be connected using DisplayPort 1.2 or HDMI 1.4a if available. HD-Audio codecs, such as Dolby TrueHD and DTS-HD, can be transmitted via bitstream mode through the HDMI port. However, as most laptops will feature Optimus, the integrated GPU will likely have direct control over the display ports and may limit the feature set available by the Nvidia Kepler cards."

Link: Intel WiDI information - If your external monitor does not have built-in WiDi support you'll also need a digital adapter AKA [Push to TV adapters, digital media hubs, digital media extenders, or digital media streamers].

 

Link: Intel Configuration FAQ's for using 3 Monitors with 3rd Generation Intel Core Processors with an Intel HD 4000/2500.