Question

X-1 sobre 6 igual 6 sobre x+4

Answer 1

Explicação passo-a-passo:

(x-1)/6=6/(x+4)

(x-1).(x+4)=6.6

x²+4x-x-4=36

x²+3x-4-36=0

x²+3x-40=0

a=1

b=3

c=-40

∆=b²-4.a.c

∆=(3)²-4.(1).(-40)

∆=9+160

∆=169

x'=[-(+3)+√169]/2.(1)

x'=[-3+13]/2

x'=10/2

x'=5

x"=[-(+3)-√169]/2.(1)

x"=[-3-13]/2

x"=-16/2

x"=-8

Resposta :

S={( -8,5)}

Answer 2

Explicação passo-a-passo:

Proporção :

$\mathsf{\dfrac{x-1}{6}~=~\dfrac{6}{x+4} }$

$\mathsf{(x-1).(x+4)~=~6.6 }$

$\mathsf{x^2+4x-x-4~=~36 }$

$\mathsf{x^2+3x-40~=~0 }$

$\mathsf{Coeficientes:}\begin{cases} a=1 \\ \\ b~=~3 \\ \\ c~=~-40 \end{cases}$

∆ = b² - 4ac

∆ = 3² - 4 • 1 • (-40)

∆ = 9 + 160

∆ = 169

$\mathsf{x_{1,2}~=~\dfrac{-b\pm\sqrt{\Delta}}{2a} }$

$\begin{cases} x_{1}~=~\dfrac{-b+\sqrt{\Delta}}{2a} \\ \\ x_{2}~=~\dfrac{-b-\sqrt{\Delta}}{2a} \end{cases}$

$\begin{cases} \mathsf{x_{1}~=~\dfrac{-3+\sqrt{169}}{2.1}=\dfrac{-3+13}{2}=\dfrac{10}{2}} \\ \\ \mathsf{x_{2}~=~\dfrac{-3-\sqrt{169}}{2.1}=\dfrac{-3-13}{2}=\dfrac{-16}{2}} \end{cases}$

$\begin{cases} \mathsf{\red{x_{1}~=~5}} \\ \\ \mathsf{\red{x_{2}~=~-8}} \end{cases}$

Espero ter ajudado bastante!)