# Name of this $u\left(x_{1}, x_{2}\right)=x_{1}+\alpha x_{2}+\beta \sqrt{x_{1} x_{2}}$ utility function?

I have seen this $$u\left(x_{1}, x_{2}\right)=x_{1}+\alpha x_{2}+\beta \sqrt{x_{1} x_{2}}$$ a numbers of time now. I wonder whether it is somehow special and therefore has it's own name?

Kind regards,

• Latex doesn’t format in question titles fyi – Brennan May 8 '20 at 21:42
• "LaTeX doesn't format", what does that mean? Everything looks fine to me. – Xenusi May 8 '20 at 21:44
• disregard my comment, LaTeX doesn't appear in titles properly on the mobile version – Brennan May 9 '20 at 1:47
• For $\alpha=\beta^2/4$ it is additively separable, but other than that I wouldn't know any special property or even name for it. – VARulle May 9 '20 at 12:43
• – VARulle May 9 '20 at 14:17