Indetermined system

$\sum _{i=1}^{N}{x}_{i}=\sum _{i=1}^{N}\frac{1}{{x}_{i}}=3$

for $N>2$. The main aspect that confuses me is the general $N$ and I'm not sure how to proceed.

$\sum _{i=1}^{N}{x}_{i}=\sum _{i=1}^{N}\frac{1}{{x}_{i}}=3$

for $N>2$. The main aspect that confuses me is the general $N$ and I'm not sure how to proceed.