Question 8
In this paper, let $\lfloor x\rfloor$ denote the greatest integer not exceeding $x$. For examples, $\lfloor5\rfloor=5$, $\lfloor2.8\rfloor=2$, and $\lfloor-2.3\rfloor=-3$.
Let $S$ be the sum of all the positive solutions of the equation $$\sqrt{\frac{4-x^2}{3}}+\sqrt{\frac{x^2-1}{3}}=1.$$ Find $\lfloor S\rfloor$.
Let $S$ be the sum of all the positive solutions of the equation $$\sqrt{\frac{4-x^2}{3}}+\sqrt{\frac{x^2-1}{3}}=1.$$ Find $\lfloor S\rfloor$.