lean_workbook_plus_57944

$a,b,c>0\iff x,y,z>0$ doesn't make difference. If the inequality $\sum{\sqrt{x^{2}+y^{2}+2z}}<\sqrt{3}$ doesn't hold for $\left( x,y,z \right) = \left( 1,0,0 \right)$ , it also doesn't hold for $\left( x,y,z\right) = \left( 1-\varepsilon,\frac{\varepsilon}{2},\frac{\varepsilon}{2}\right)$ , where $\varepsilon>0$ is near $0$ (and such triples satisfy condition $x,y,z>0$ ), so the inequality $\sum{\sqrt{x^{2}+y^{2}+2z}}<\sqrt{3}$ isn't true.