1978 IMO 第 4 题

(CZS 2) Let $T_{1}$ be a triangle having $a, b, c$ as lengths of its sides and let $T_{2}$ be another triangle having $u, v, w$ as lengths of its sides. If $P, Q$ are the areas of the two triangles, prove that $$16 P Q \leq a^{2}\left(-u^{2}+v^{2}+w^{2}\right)+b^{2}\left(u^{2}-v^{2}+w^{2}\right)+c^{2}\left(u^{2}+v^{2}-w^{2}\right)$$ When does equality hold?

(CZS 2) 令$T_{1}$为一个边长为$a、b、c$的三角形，并令$T_{2}$为另一个边长为$u、v、w$的三角形。如果$P, Q$是两个三角形的面积，证明 $$16 P Q \leq a^{2}\left(-u^{2}+v^{2}+w^{2}\right)+b^{2}\left(u^{2}-v^{2}+w^{2}\right)+c^{2}\left(u^{2}+v^{2}-w^{2}\right)$$ 当平等成立吗？