H-R diagram, Double stars Can someone help me? I have a case, like, we have H-R diagram and two stars on it. One of them is a blue star on main sequence, another is a red giant. They have equal luminosity. If they are in a double star system and seen from Earh as one star, then where on the diagram should I place this star? What luminosity amd temperature will it have?

Maybe I should sum up their luminosity and then, using Stefan Boltzmann law, calculate the temperature? But does the law work for red giants? And can I sum the luminosity?
"Maybe I should sum up their luminosity and then, using Stefan Boltzmann law, calculate the temperature? But does the law work for red giants? And can I sum the luminosity?"

This answer is not about placing the object on HR diagram, but is about the characteristic temperature as a blackbody.

It seems like you have a point source which you know that it is a combination of two stars: one blue, and the other redder. You can apply two-component blackbody: $F_{\lambda,total} = C_1 \times F_{\lambda,1}(T_1) + C_2 \times F_{\lambda,2}(T_2) ; T_1 \ne T_2$ where $F_{\lambda,total}$ is the observed specific fluxes from the point source, $F_{\lambda,1}, F_{\lambda,2}$ are blackbodies with temperature $T_1, T_2$ respectively, $C$s are normalization constants.

Blackbody approximately (to the first order) works with stars including red giants as long as you include a portion of the SED where the line absorption/emission is negligible. For example, some stars have strong absorption at less than 4000 A due to metals, therefore that portion deviates significantly from the blackbody.

You can sum fluxes, since fluxes are normalized for the luminosity distance. Since luminosity $L$ is $L = F \times 4 \pi D_L^2$ where $D_L$ is the luminosity distance, the total luminosity is $L_1 + L_2 = 4 \pi D_{L,1}^2 \times F_1 + 4 \pi D_{L,2}^2 \times F_2 = C_1 \times F_1 + C_2 \times F_2$. Therefore, you can sum the luminosity when $D_{L,1} \approx D_{L,2}$.