Question

va rlg ajutati-ma cu exercitiul 24, B si C​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

E(x) = x^3 + x^2 - 4x - 4 = x^2*(x + 1) - 4*(x + 1) = (x + 1)(x^2 - 4)

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

F(x) = x^3 + 2x^2 - x - 2 = x^2*(x + 2) - (x + 2) = (x + 2)(x^2 - 1)

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

b)

E(x)/F(x) = (x + 1)(x + 2)(x - 2)/(x + 2)(x - 1)(x + 1) = (x - 2)/(x - 1)

x + 2 ≠ 0 ⇒ x ≠ -2

x - 1 ≠ 0 ⇒ x ≠ 1

x + 1 ≠ 0 ⇒ x ≠ -1

x ∈ R \ {-2, -1, 1}

c)

(x + 1)(x + 2)(x - 2) + (x + 2)(x - 1)(x + 1) = 0

(x + 1)(x + 2)(x - 2 + x - 1) = 0

(x + 1)(x + 2)(2x - 3) = 0

x + 1 = 0 ⇒ x = -1

x + 2 = 0 ⇒ x = -2

2x - 3 = 0 ⇒ x = 3/2

A = {-2, -1, 3/2}