ma poate ajuta cineva sa rezolve acest exercitiu,va rog frumos!am nevoie multa de rezolvare!va multumesc!​

Răspuns:

Explicație pas cu pas:

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)

______________

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

x ≠ -2; -1; 1

_______________

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

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

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

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

un produs este egal cu 0 daca unul din factori este 0

x + 1 = 0 ⇒ x = -1

x = 2 = 0 ⇒ x = -2

2x - 3 = 0 ⇒ x = 3/2

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

a) E(x) = x³+x²-4x-4 =x²(x-1) -4(x+1) = (x+1)(x²-4) = (x+1)(x+2)(x-2)

F(x) = x²(x+2) - (x+2) = (x+2)(x²-1) = (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)

c) E(x) + F(x) = x³+x²-4x-4 + x³+2x²-x-2 = 2x³+3x²-5x -6

2x³+3x²-5x-6 = 0

2x³+2x² + x²+x -6x-6 = 0

2x²(x+1) +x(x+1) -6(x+1) =0

(x+1)(2x²+x-6) = 0

(x+1)(2x²+4x-3x-6) =0

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

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

x+1 = 0, x= -1

x+2 = 0 , x = -2

2x-3 =0, x = 3/2

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