Question 98
Let $a \leq b \leq c \leq d$ be real numbers such that
$$
a+b+c+d=0 \quad \text{ and } \quad \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}=0
$$
Prove that $a+d=0$.
$$
a+b+c+d=0 \quad \text{ and } \quad \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}=0
$$
Prove that $a+d=0$.