Question

E urgent! Ex 5 pls repede

Answer 1

Răspuns:

Explicație pas cu pas:

a)

$\frac{4n+7}{2n-1} =\frac{2(2n-1)+9}{2n-1} =\frac{2(2n-1)}{2n-1}+\frac{9}{2n-1}=\\ \\ \\=2+\frac{9}{2n-1}$

2n - 1  ∈ {-9, -3, -1, 1, 3, 9} ⇔ 2n ∈ {-8, -2, 0, 2, 4, 10}

⇔ n ∈ {-4, -1, 0, 1, 2, 5}, n ≠ 0

⇒ n ∈ {-4, -1, 1, 2, 5}

b)

$\frac{7n+13}{2n-1} =\frac{3(2n-1) +n+16}{2n-1} =3+\frac{n+16}{2n-1}$

n + 16 ≥ 2n - 1 ⇔ n ≤ 17   &   (n + 16) | (2n - 1)

n = 17:    33 | 33

n = 6:     22 | 11

n = 2:      18 |  3

n = 1:       17 |  1

n = 0:      16 | -1, nevalid n ≠ 0

n = -1:      15 | -3

n = -5:      11 | -11

⇒ n ∈ {-5, -1, 1, 2, 6, 17}