Question

e) Nesse item, calcule x.

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\textsf{Pelo teorema da bissetriz interna, temos que:}$

$\sf{\dfrac{4}{2} = \dfrac{\overline{\rm AC}}{x}}$

$\sf{\overline{\rm AC} = 2x}$

$\sf{(\overline{\rm AC})^2 = (\overline{\rm AB})^2 + (\overline{\rm BC})^2 }$

$\sf{(2x)^2 = 4^2 + (2 + x)^2}$

$\sf{4x^2 = 16 + (4 + 4x + x^2)}$

$\sf{3x^2 - 4x - 20 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (-4)^2 - 4.3.(-20)}$

$\mathsf{\Delta = 16 + 240}$

$\mathsf{\Delta = 256}$

$\sf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{4 \pm \sqrt{256}}{6} \rightarrow \begin{cases}\sf{x' = \dfrac{4 + 16}{6} = \dfrac{20}{6} = \dfrac{10}{3}}\\\\\sf{x'' = \dfrac{4 - 16}{6} = -\dfrac{12}{6} = -2}\end{cases}}$

$\boxed{\boxed{\sf{x = \dfrac{10}{3}}}}$