Question

Aflati numarul natural stiind ca x/2=8/x : 3/x=x/12 ; x/3=27/x; 20/x=x/5;x/4=9/x

Answer 1

$x\in \mathbb_{N} \\ \\ 1) \dfrac{x}{2} = \dfrac{8}{x} \Rightarrow x^2 = 16 \Rightarrow x = 4 \\ \\ 2) \dfrac{3}{x} = \dfrac{x}{12} \Rightarrow x^2 = 3\cdot 12\Rightarrow x^2 = 36 \Rightarrow x = 6 \\ \\ 3) \dfrac{x}{3} = \dfrac{27}{x} \Rightarrow x^2 = 3\cdot 27\Rightarrow x^2 = 81 \Rightarrow x = 9 \\ \\ 4) \dfrac{20}{x} = \dfrac{x}{5} \Rightarrow x^2 = 5\cdot 20\Rightarrow x^2 = 100 \Rightarrow x = 10$
$5) \dfrac{x}{4} = \dfrac{9}{x} \Rightarrow x^2 = 9\cdot 3\Rightarrow x^2 = 36 \Rightarrow x = 6$