Question 99
Let $a \geqslant b \geqslant c \geqslant d$ be real numbers such that
$$
(a-b)(b-c)(c-d)(d-a) = -3
$$
a) If $a+b+c+d=6$, prove that $d \lt 0.36$.
b) If $a^{2}+b^{2}+c^{2}+d^{2}=14$, show that $(a+c)(b+d) \leqslant 8$. Determine the cases of equality.
$$
(a-b)(b-c)(c-d)(d-a) = -3
$$
a) If $a+b+c+d=6$, prove that $d \lt 0.36$.
b) If $a^{2}+b^{2}+c^{2}+d^{2}=14$, show that $(a+c)(b+d) \leqslant 8$. Determine the cases of equality.