Question

(Souza Marques) A raiz positiva da equação 1/x-2 - 2/x-1 =1 e: ??

Answer 1

1/(x-2) - 2/(x-1) = 1

1(x-1)/(x-2)(x-1) -2(x-2)/(x-1)(x-2) = 1

(x-1) - (x-2) / (x-1)(x-2) = 1

x -1 -x +2 = (x-1)(x-2)

(x-1)(x-2) = 1

x²-2x-x+2=1

x²-3x+3=0

∆=(-3)²-4(1)(3)
∆=9-12
∆=-3

x=-(-3)±√-3/2
x=3±i√3/2