Question

Determinati numerele naturale a si b, astfel încat (a+2) × (b-3) =28 AM NEVOIE URGENT!!!!​

Answer 1

Răspuns:

(a,b) ∈ {(0,17), (2,10), (5,7), (12,5), (26,4)}

Explicație pas cu pas:

(a+2) × (b-3) = 28

28 = 1 × 28 = 2 × 14 = 4 × 7 = 7 × 4 = 14 × 2 = 28 × 1

=>

1) a + 2 = 1 <=> a = -1 ∉ N

2) a + 2 = 2 => a = 0

b - 3 = 14 => b = 17

3) a + 2 = 4 => a = 2

b - 3 = 7 => b = 10

4) a + 2 = 7 => a = 5

b - 3 = 4 => b = 7

5) a + 2 = 14 => a = 12

b - 3 = 2 => b = 5

6) a + 2 = 28 => a = 26

b - 3 = 1 => b = 4

→ (a,b) ∈ {(0,17), (2,10), (5,7), (12,5), (26,4)}

Answer 2

$\it a\in\mathbb{N} \Rightarrow a\geq0\Big|_{+2} \Rightarrow a+2 \geq 2 \\ \\ (a+2)(b-3)=28=2\cdot14=4\cdot7=7\cdot4=14\cdot2=28\cdot1\\ \\ a+2\in\{2,\ 4,\ 7,\ 14,\ 28\}\big|_{-2} \Rightarrow a\in\{0,\ 2,\ 5,\ 12,\ 26\}\\ \\ b-3\in\{14,\ 7,\ 4,\ 2,\ 1\}\Big|_{+3} \Rightarrow b\in\{17,\ 10,\ 7,\ 5,\ 4\}\\ \\ \\ (a,\ b)\in\{(0,\ 17);\ (2,\ 10);\ (5,\ 7);\ (12,\ 5);\ (26,\ 4)\}$