Question

Arătați ca numarul x este natural unde: !Va rog ,dau coroana

Answer 1

$x = \sqrt{\dfrac{19}{2,(1)}} +\sqrt{\dfrac{20}{2,(2)}}+\sqrt{\dfrac{21}{2,(3)}} +...+\sqrt{\dfrac{26}{2,(8)}} \\ \\ \\x=\sqrt{\dfrac{19}{\dfrac{21-2}{9}}}+\sqrt{\dfrac{20}{\dfrac{22-2}{9}}}+ \sqrt{\dfrac{21}{\dfrac{23-2}{9}}} + ... +\sqrt{\dfrac{26}{\dfrac{28-2}{9}}}\\ \\\\ x=\sqrt{\dfrac{19}{\dfrac{19}{9}}}+\sqrt{\dfrac{20}{\dfrac{20}{9}}}+ \sqrt{\dfrac{21}{\dfrac{21}{9}}} + ... +\sqrt{\dfrac{26}{\dfrac{26}{9}}}\\ \\ \\ x=\sqrt{9}+\sqrt{9}+\sqrt{9}+...+\sqrt{9}$

$x = 8\cdot \sqrt{9}\\ \\ x = 8\cdot 3\\ \\ \Rightarrow x = 24\in \mathbb{N}$