Question

alguém consegue resolver esse teorema de tales urgente?!

Answer 1

Resposta:

$\dfrac{x}{x+6}=\dfrac{x+2}{2x+7}\\ \\ multiplica~~cruzado\\ \\ \\ x.(2x+7)=(x+6)(x+2)\\ \\ 2x^2+7x=x^2+8x+12\\ \\ 2x^2-x^2+7x-8x-12=0\\ \\\\ x^2-x-12=0\\ \\ a=1\\ b=-1\\ c=-12\\ \\ \\ \Delta=b^2-4ac\\ \Delta=(-1)^2-4(1)(-12)\\ \Delta=1+48\\ \\ \Delta=49$

$x=\dfrac{-b\pm\sqrt{\Delta} }{2a}\\ \\ x=\dfrac{-(-1)\pm\sqrt{49} }{2(1)}=\dfrac{1\pm7}{2}\\ \\ \\ x'=\dfrac{1+7}{2}=\dfrac{8}{2}=4\\ \\ \\ x"=\dfrac{1-7}{2}=-\dfrac{6}{2}=-3\to n/serve$

Logo x = 4