Question

como resolver essas equações do 2 grau? A) x-5= -1/x-3
B) y+3= 72/y-1

Answer 1

A)
$x - 5 = \frac{ - 1}{x - 3}$
$(x - 5) \times (x - 3) = - 1$
${x}^{2} - 8x + 15 = - 1$

${x}^{2} - 8x + 15 + 1 = 0$
${ x}^{2} - 8x + 16 = 0$
∆ = (-8)² -4 . 1 . 16

∆ = 64 - 64

∆ = 0

$x = \frac{ - ( - 8) + - \sqrt{0} }{2}$
$x = \frac{8}{2}$
S = {8,8}

B)
$y + 3 = \frac{72}{y - 1}$
$(y + 3) \times (y - 1) = 72$
${y}^{2} + 2y - 3 = 72$

${y}^{2} + 2y - 3 - 72 = 0$

${y}^{2} + 2y - 75 = 0$
∆ = 2² - 4.1.(-75)

∆ = 4 + 300

∆ = 304

x = (-2 +- √ 304)/2

x = (-2 +- √2².2².19)/2
x = (-2 +- 4√19)/2

x1 = (-2 + 4√19)/2

x1 = -1 +2√19

x2 = (-2 -4√19)/2

x2 = -1 -2√19

S = {- 1 - 2√19, - 1 + 2√19}