Question

Calculati x......
multumesc anticipat​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Răspuns:

2

Explicație pas cu pas:

$x = \sqrt{80 \cdot 82 \cdot \Big[ \Big( \dfrac{2}{1 \cdot 3} + \dfrac{2}{3 \cdot 5} + ... + \dfrac{2}{39 \cdot 41}\Big) - \Big( \dfrac{3}{1 \cdot 4} + \dfrac{3}{4 \cdot 7} + ... + \dfrac{3}{37 \cdot 40}\Big)} =$

$= \sqrt{80 \cdot 82 \cdot \Big[ \Big( \dfrac{3 - 1}{1 \cdot 3} + \dfrac{5 - 3}{3 \cdot 5} + ... + \dfrac{41 - 39}{39 \cdot 41}\Big) - \Big( \dfrac{4 - 1}{1 \cdot 4} + \dfrac{7 - 4}{4 \cdot 7} + ... + \dfrac{40 - 37}{37 \cdot 40}\Big)}$

$= \sqrt{80 \cdot 82 \cdot \Big[ \Big( \dfrac{1}{1} - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{5} + ... + \dfrac{1}{39} - \dfrac{1}{41}\Big) - \Big( \dfrac{1}{1} - \dfrac{1}{4} + \dfrac{1}{4} - \dfrac{1}{7} + ... + \dfrac{1}{37} - \dfrac{1}{40}\Big)}$

$= \sqrt{80 \cdot 82 \cdot \Big[ \Big( \dfrac{1}{1} - \dfrac{1}{41}\Big) - \Big( \dfrac{1}{1} - \dfrac{1}{40}\Big)}$

$= \sqrt{80 \cdot 82 \cdot \Big(\dfrac{41 - 1}{41} - \dfrac{40 - 1}{40}\Big)}$

$= \sqrt{80 \cdot 82 \cdot \Big(\dfrac{40}{41} - \dfrac{39}{40}\Big)} = \sqrt{80 \cdot 82 \cdot \dfrac{ {40}^{2} - 39 \cdot 41}{40 \cdot 41}}$

$= \sqrt{2 \cdot 2 \cdot (1600 - 1599)} = \sqrt{ {2}^{2} \cdot 1} = \sqrt{ {2}^{2} } = \bf 2$