Question

Am nevoie de punctul b de la problema din poza va rog!!!

Answer 1

Explicație pas cu pas:

b)

$\frac{1}{m} + \frac{1}{n} = \frac{1}{2021} \implies \frac{m + n}{mn} = \frac{1}{2021} \\ \iff m + n = \frac{mn}{2021}$

43 × 47 = 2021

$\sqrt{\Big( \frac{m}{43} - 47\Big)\Big( \frac{n}{47} - 43\Big)} = \sqrt{ \frac{mn}{2021} - m - n + 43 \cdot 47 } = \\ = \sqrt{m + n - m - n + 43 \cdot 47} = \bf \sqrt{43 \cdot 47} \not \in \mathbb{N}$

q.e.d.