Question

Sabendo que as retas a, b e c são paralelas, utilize o Teorema de Tales e determine o valor de x na figura a seguir:

Answer 1

$\large\boxed{\begin{array}{l}\sf\dfrac{3x}{x+6}=\dfrac{x+3}{x}\\\\\sf 3x^2= (x+6)\cdot(x+3)\\\sf 3x^2=x^2+9x+18\\\sf 3x^2-x^2-9x-18=0\\\sf 2x^2-9x-18=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-9)^2-4\cdot2\cdot(-18)\\\sf\Delta=81+144\\\sf\Delta=225\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-(-9)\pm\sqrt{225}}{2\cdot2}\\\\\sf x=\dfrac{9\pm15}{4}\begin{cases}\sf x_1=\dfrac{9+15}{4}=\dfrac{24}{4}=6\\\\\sf x_2=\dfrac{9-15}{4}=-\dfrac{6\div2}{4\div2}=-\dfrac{3}{2}\end{cases}\\\\\sf resposta:x=6\end{array}}$