Cho $\it{3}$ số thực $\it{a},\,\it{b},\,\it{c}$ thỏa mãn $\it{:}$ $\it{a}^{\,\it{2}}+ \it{b}^{\,\it{2}}+ \it{c}^{\,\it{2}}= \it{1}$ $\it{.}$ Chứng minh rằng $\it{:}$
$$\frac{\it{bc}}{\it{a}^{\,\it{2}}+ \it{1}}+ \frac{\it{ca}}{\it{b}^{\,\it{2}}+ \it{1}}+ \frac{\it{ab}}{\it{c}^{\,\it{2}}+ \it{1}}\geqq -\,\frac{\it{1}}{\it{2}}$$
Spoiler
