Question

2) Sabendo que as retas a, b e c são paralelas, determine o valor de x.​

Answer 1

Resposta:

x=3

Explicação passo-a-passo:

Teorema de Tales:

6/(2x+4)=2x/(2x+4)

Multiplicando em cruz

6.(2x+4)=2x.(2x+4)

12x+24=4x²+8x

4x²+8x-12x-24=0

4x²-4x-24=0 ÷(4)

x²-x-6=0

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-x-6=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=-1~e~c=-6\\\\C\'alculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-1)^{2}-4(1)(-6)=1-(-24)=25\\\\C\'alculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-1)-\sqrt{25}}{2(1)}=\frac{1-5}{2}=\frac{-4}{2}=-2\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-1)+\sqrt{25}}{2(1)}=\frac{1+5}{2}=\frac{6}{2}=3\\\\S=\{-2,~3\}$

Descartar x= -2 porque não existe lado negativo (2x=2.(-2)=-4)

x=3