Question

determinati nr real x stiind ca x/2√3=8√3/x​

Answer 1

Răspuns:

$\dfrac{x}{2 \sqrt{3} }=\dfrac{8 \sqrt{3} }{x} \implies x \cdot x= 2 \sqrt{3}\cdot 8\sqrt{3}$

$x^{2} = 16 \sqrt{3}\cdot \sqrt{3}$

$x^{2} = 16\cdot3$

$x^{2} = 48 \implies x = \pm \sqrt{48} \implies$

$x = \pm 4\sqrt{3} \implies$

$\red{x_{1} = + \: 4\sqrt{3} }$

$\red{x_{2} = - \: 4\sqrt{3} }$

Answer 2

$\it \dfrac{x}{\ \ 2\sqrt3}=\dfrac{8\sqrt3}{x}\Big|_{\cdot\sqrt3} \Rightarrow \dfrac{x}{2}=\dfrac{24}{x}\Rightarrow x^2=48 \Rightarrow \sqrt{x^2}=\sqrt{48} \Rightarrow \\ \\ \\ \Rightarrow |x|=\sqrt{16\cdot3} \Rightarrow x=\pm4\sqrt3 \Rightarrow x_1=-4\sqrt3,\ \ x_2=4\sqrt3.$