Question

determinati numarul natural a astfel incat a+2 supra a+3 sa fie mai mare sau egal cu 5 supra 9

Answer 1

Răspuns:

Explicație pas cu pas:

(a + 2)/(a + 3) ≥ 5/9

9(a + 2) ≥ 5(a + 3)

9a + 18 ≥ 5a + 15

9a - 5a ≥ 15 - 18

4a ≥ -3

a ≥ -3/4

a = 0, 1, 2,... (orice numar natural)

Answer 2

$\it \dfrac{a+2}{a+3}=\dfrac{a+3-1}{a+3}=\dfrac{a+3}{a+3}-\dfrac{1}{a+3}=1-\dfrac{1}{a+3}\geq1-\dfrac{1}{0+3} \Rightarrow\\ \\ \\ \Rightarrow\dfrac{a+2}{a+3}\geq1-\dfrac{1}{3}=\dfrac{^{3)}2}{\ 3}=\dfrac{6}{9}\geq\dfrac{5}{9},\ \ \forall\ a\in\mathbb{N}$