Rozwiązane

Rozwiąż równanie:
[tex]\frac{x-5}{x+1} - 1 = x+1[/tex]



Odpowiedź :

(x - 5)/(x + 1) - 1 = x + 1

x ≠ -1

(x - 5)/(x + 1) = x + 1 + 1

(x - 5)/(x + 1) = x + 2

(x + 1)(x + 2) = x - 5

x² + 2x + x + 2 = x - 5

x² + 3x + 2 = x - 5

x² + 3x + 2 - x + 5 = 0

x² + 2x + 7 = 0

a = 1, b = 2, c = -7

∆ = 2² - 4 * 1 * (-7) = 4 + 28 = 32

√∆ = √32 = 4√2

x = (-2 - 4√2)/2 = -1 - 2√2

x = (-2 + 4√2)/2 = -1 + 2√2