Q. Is there a way to make Radeon or Nvidia graphics work in my dual-GPU laptop?
Not if the discrete card is not dedicated (eg. tied to the Intel device).
The discrete graphics capability in a switched dual-GPU configuration is not supported with OS X on hacks. Best you can do is disable the discrete part with SSDT/DSDT patches. See the prior question.
If your discrete device (AMD Radeon or Nvidia) is not routed through the Intel GPU, then it is considered dedicated. Some laptops have the internal display connected to the Intel GPU and the external HDMI/DP port connected to the discrete graphics device. It is rare, but in that case you would be able to get the device to work with the external display with proper kexts and correct configuration, much like a dual-GPU desktop setup.