$$ex sqrt{x^2+x+1}+ sqrt{y^2+y+1} +sqrt{x^2-x+1}+ sqrt{y^2-y+1}geq 2(x+y). eex$$ Ref. [Proof Without Words: An Algebraic Inequality, The College Mathematics Journal].
$$ex sqrt{x^2+x+1}+ sqrt{y^2+y+1} +sqrt{x^2-x+1}+ sqrt{y^2-y+1}geq 2(x+y). eex$$ Ref. [Proof Without Words: An Algebraic Inequality, The College Mathematics Journal].