Question

Calcule o valor x, sabendo que as retas a, b e c são paralelas​

Answer 1

Explicação passo-a-passo:

Pelo Teorema de Tales:

$\sf \dfrac{3x}{x+6}=\dfrac{x+3}{x}$

$\sf 3x\cdot x=(x+6)\cdot(x+3)$

$\sf 3x^2=x^2+3x+6x+18$

$\sf 3x^2=x^2+9x+18$

$\sf 3x^2-x^2-9x-18=0$

$\sf 2x^2-9x-18=0$

$\sf \Delta=(-9)^2-4\cdot2\cdot(-18)$

$\sf \Delta=81+144$

$\sf \Delta=225$

$\sf x=\dfrac{-(-9)\pm\sqrt{225}}{2\cdot2}=\dfrac{9\pm15}{4}$

$\sf x'=\dfrac{9+15}{4}~\Rightarrow~x'=\dfrac{24}{4}~\Rightarrow~\red{x'=6}$

$\sf x"=\dfrac{9-15}{4}~\Rightarrow~x"=\dfrac{-6}{4}~\Rightarrow~\red{x"=\dfrac{-3}{2}}$ (não serve)

Logo, x = 6