Question

Encontre o valor de x na expressão: $\frac{3-x}{x}$= 3·$\frac{\sqrt{13} +3}{6}$

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{\dfrac{3-x}{x} = 3\left(\dfrac{\sqrt{13} + 3}{6}\right)}$

$\mathsf{\dfrac{3-x}{x} = \left(\dfrac{\sqrt{13} + 3}{2}\right)}$

$\mathsf{6-2x = x\sqrt{13} + 3x}$

$\mathsf{6 = x\sqrt{13} + 5x}$

$\mathsf{6 = x(\sqrt{13} + 5)}$

$\mathsf{x = \dfrac{6}{\sqrt{13} + 5}}$

$\mathsf{x = \left(\dfrac{6}{\sqrt{13} + 5}\right) \times \left(\dfrac{\sqrt{13} - 5}{\sqrt{13} - 5}\right)}$

$\mathsf{x = \dfrac{6\sqrt{13} - 30}{13 - 25}}$

$\mathsf{x = -\dfrac{6\sqrt{13} - 30}{12}}$

$\boxed{\boxed{\mathsf{x = \dfrac{5 - \sqrt{13}}{2}}}}$