Question

resolva as equações:

a) x+1 = 24/x-1 com x diferente de 1

b) (x-2)(x-4) = -6x + 12

Answer 1

a)

$x+1 = 24/x-1$

$(x+1)(x-1) = 24$

$x^2-1^2=24$

$x^2-1=24$

$x^2=24+1 =25$

$x= \pm \sqrt{25}$

$x= \pm 5$

b)

$(x-2)(x-4) = -6x + 12$

$x^2-4x-2x+8=-6x+12$

$x^2-6x+8=-6x+12$

$x^2-6x+6x=12+8$

$x^2=20$

$x= \pm \sqrt {20}$

$x= \pm \sqrt {4 \cdot 5}$

$x= \pm \sqrt {4} \cdot \sqrt { 5}$

$x= \pm 2\sqrt {5}$