Question

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Answer 1

Explicație pas cu pas:

x ∈ N, F ∈ N

a)

$F = \frac{8}{x + 1}$

x + 1 > 0

(x + 1) este divizor al lui 8

(x + 1) ∈ {1; 2; 4; 8}

$x + 1 = 1 = > x = 1 - 1 = > x = 0 \\ x + 1 = 2 = > x = 2 - 1 = > x = 1 \\ x + 1 = 4 = > x = 4 - 1 = > x = 3 \\ x + 1 = 8 = > x = 8 - 1 = > x = 7$

=> x ∈ {0; 1; 3; 7}

b)

$F = \frac{2x + 7}{x + 2} = \frac{2x + 4 + 3}{x + 2} = \frac{2(x + 2) + 3}{x + 2} \\ = 2 + \frac{3}{x + 2}$

x + 2 > 0

(x + 2) este divizor al lui 3

(x + 2) ∈ {1; 3}

$x + 2 = 1 = > x = 1 - 2 = > x = - 1 \\ x + 2 = 3 = > x = 3 - 2 = > x = 1$

-1 ∉ N => x = 1