The two stars will look like a single point of light. The two stars will appear to be touching, rather like a small dumbell. You will be able to see two distinct stars. You will see only the larger of the two stars, and not the smaller one. The theoretical resolving power of a telescope scales inversely as the focal length.
Radio telescopes are generally smaller than optical telescopes.
The radiation from an x-ray telescope presents a health hazard to astronomers. Gamma ray telescopes can be located on the Earth's surface. Infrared telescopes need to be launched into space. Telescopes in space are cheap to construct and easy to maintain. Spectroscopy is the analysis of the intensity of light at each wavelength.