Question

A soma das raízes da equação modular |x+1|^2 - 5|x+1| +4 = 0 é ????

Answer 1

             Trata-se de uma equação do segundo grau em (x + 1)

             Introduzir mudança de variável
                      x + 1 = z
                                            z = x + 1 > 0   Condição de existencia
            A equação fica
                                       z^2 - 5z + 4 = 0
           Resolvendo
                                        (z - 4)(z - 1) = 0
                                                   z1 = 4
                                                   z2 = 1
           Voltando à variável original
                                        x + 1 = 4
                                              x = 3
                                    - (x + 1) = 4
                                       - x - 1 = 4
                                           - x = 5
                                             x = - 5    DESCONSIDERAR (- 5 < 0)
                                                             x = 3   RAIZ

                                        x + 1 = 1
                                              x = 0
                                      - (x + 1) = 1
                                           - x - 1 = 1
                                               - x = 2
                                                 x = - 2  DESCONSIDERA  (- 2 < 0)
                                                              x = 0  RIAZ

                                                                                          S = { 0, 3 }

                                                                                              SOMA RAÍZES = 3  (0 + 3)

Answer 2

Resposta:

-4

Explicação passo-a-passo:

A soma das raízes da equação modular | x + 1|² - 5| x + 1| + 4 = 0   é

| x + 1 | = K  

K²-5K+4

K1 = 1      K2 = 4

| x + 1 | = 1

x+1 = 1

x = 0

x+1 = -1

x= - 2

| x + 1 | = 4

x+1 = 4

x = 3

x+1 = -4

x = -5

Somando as raízes:    -5 + (-2) + 3 + 0 =  -7+3 = -4