Question

20 BALL!!!!!!!!!!!!!!!!!!!!!PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!

Answer 1

Olá Asa

1/(x*(x + 2)) - 1/(x + 1)² = 1/12

12/(x*(x + 2)) - 12(x + 1)² = 1

12*(x + 1)² - 12*x*(x + 2) = x*(x + 2)*(x + 1)²

12x² + 24x + 12 - 12x² - 24x = x*(x + 2)*(x² + 2x + 1)

12 = x⁴ + 4x³ + 5x² + 2x

x⁴ + 4x³ + 5x² + 2x - 12 = 0 

raiz trivial x = 1

(x⁴ + 4x³ + 5x² + 2x - 12)/(x - 1) = x³ + 5x² +10x + 12 

x³ + 5x² +10x + 12 = 0 

outra raiz trivial x = -3

(x³ + 5x² +10x + 12)/(x + 3) = x² + 2x + 4 

duas raízes reais

x1 = 1
x2 = -3