Question

resolver a inequação quociente: (x²-3)/(x+3) ≤ 1
a) S = { X e R | < -3 ou -2 ≤ x ≤ 3}
b) S = { X e R | < -1 ou -2 ≤ x ≤ 3}
c) S = { X e R | < -3 ou -1 ≤ x ≤ 2}
d) S = { X e R | < -1 ou -2 ≤ x ≤ 2}

Answer 1

Resposta:

(x²-3)/(x+3) ≤ 1

(x²-3)/(x+3) - 1 ≤ 0

(x²-3-x-3)/(x+3) ≤ 0

(x²-x-6)/(x+3) ≤ 0

q=x²-x-6  

raízes ==>x'=(1+5)/2=3  ou x''=(1-5)/2=-2

q+++++++++++++(-2)---------------------------(3)+++++++++++++++

p=x+3  ..raiz x'=-3    

p-----------------------------(-3)++++++++++++++++++++++++

Estudo de sinais:

q+++++++++++++++++(-2)---------------(3)+++++++++++++++

p---------------(-3)++++++++++++++++++++++++++++++++++

q/p------------(-3)+++++(-2)---------------(3)+++++++++++++++

(-∞,-3) U [-2,3]    ou   S = { X ∈ R | < -3 ou -2 ≤ x ≤ 3}

Letra A