Question

Utilizado a Teorema de Tales, encontre as valores de x, sabendo que as retas a, b e c são paralelas ​

Answer 1

$\large\boxed{\begin{array}{l}\sf\dfrac{x}{2}=\dfrac{4}{x+2}\\\\\sf x^2+2x=8\\\sf x^2+2x-8=0\\\sf\Delta=b^2-4ac\\\sf\Delta=2^2-4\cdot1\cdot(-8)\\\sf \Delta=4+32\\\sf\Delta=36\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-2\pm\sqrt{36}}{2\cdot1}\\\\\sf x=\dfrac{-2\pm6}{2}\begin{cases}\sf x_1=\dfrac{-2+6}{2}=\dfrac{4}{2}=2\\\\\sf x_2=\dfrac{-2-6}{2}=-\dfrac{8}{2}=-4\end{cases}\\\\\sf como~x>0,a~resposta~\acute e~2.\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~b}}}}\end{array}}$