Question

03. Determine o valor de x nos triángulos abaixo:​

Answer 1

Resposta:

x = 6

Explicação passo-a-passo:

AD/AE = AB/AC

(X-1)/(X+4) = (X+2)/(2X+4)

(X-1)*(2X+4) = (X+2)*(X+4)

2$x^{2}$+4x-2x-4 = $x^{2}$+4x+2x+8

$x^{2}$ -4x -12 = 0

x' = -b +√b2 - 4ac / 2a

x' = 4 +√16 - 4*1*-12 / 2*1

x' = 4 +8 / 2

x' = 6

Answer 2

$\frac{x - 1}{3} = \frac{x + 4}{x} \\ {x}^{2} - x = 3x + 12 \\{x}^{2} - x - 3x - 12 = 0 \\{x}^{2} - 4x - 12$

$\mathsf{\Delta=16+48=64}\\\mathsf{x=\dfrac{4\pm8}{2}}\\\mathsf{x=\dfrac{4+8}{2}=6}$

$\frac{x + 4}{x + 1} = \frac{6}{x - 1} \\ {x}^{2} + 3x - 4 = 6x + 6 \\ {x}^{2} + 3x - 6x - 4 - 6 = 0$

${x}^{2} - 3x - 10 = 0$

$\mathsf{\Delta=9+40=49}\\\mathsf{x=\dfrac{3\pm7}{2}}\\\mathsf{x=5}$