Question

va rog calculați
$\frac{ x}{8 - x} = \frac{1}{ \sqrt{3} }$
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Answer 1

$\frac{ x}{8 - x} = \frac{1}{ \sqrt{3} } < = > \\ x \sqrt{3} = 8 - x \\ x \sqrt{3} + x = 8 < = > \\ x( \sqrt{3} + 1) = 8 | \div 8 = > \\ x = ^{ \sqrt{3} - 1 )} \frac{8}{ \sqrt{3} + 1} < = > \\ x = 4( \sqrt{3} - 1) = > x = 4 \sqrt{3} - 4$

Answer 2

Răspuns: $\bf x = 4\sqrt{3}-4$

Explicație pas cu pas:

Salutare!

$\bf \dfrac{x}{8-x}=\dfrac{1}{\sqrt{3}}$

$\bf \dfrac{x}{8-x}=\dfrac{1\cdot\sqrt{3}}{\sqrt{3}\cdot\sqrt{3}}$

$\bf \dfrac{x}{8-x}=\dfrac{\sqrt{3}}{3}$

facem produsul mezilor egal cu produsul extremilor

$\bf 3x = \sqrt{3} \cdot (8-x)$

$\bf 3x = 8\sqrt{3} -\sqrt{3} x$

$\bf 3x +\sqrt{3} x= 8\sqrt{3}$

$\bf x \cdot(3 +\sqrt{3}) = 8\sqrt{3}$

$\bf x = \dfrac{8\sqrt{3} }{3 +\sqrt{3}}$

$\bf x = \dfrac{8\sqrt{3}\cdot (3 -\sqrt{3} ) }{(3 +\sqrt{3})\cdot (3 -\sqrt{3} )}$

$\bf x = \dfrac{12\sqrt{3}-12}{3}$

$\bf x = \dfrac{3 \cdot(4\sqrt{3}-4)}{3}$

$\bf x = \dfrac{\not 3 \cdot(4\sqrt{3}-4)}{\not3}$

$\boxed{\bf x = 4\sqrt{3}-4}$

sau

$\boxed{\bf x = 4\cdot(\sqrt{3}-1)}$

==pav38==