Question

determinati toate nr de forma ab stiind ca a5b e mai mare decat 754. DAU COROANA! (urgent)​

Answer 1

Salutare!

        Cerinta:

"Determinati toate numerele de forma ab stiind ca a5b e mai mare decat 754"

        Rezolvare:

$\bf \overline{ab}$ = ???

a,b - cifre

cifrele sunt: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

a,b,c,d ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

a ≠ 0 (deoarece un numar nu poate incepe cu cifra zero)

$\bf 754>\overline{a5b} \implies$ a ≥ 7

a ≥ 7 ⇒ a ∈ {7, 8, 9}

Analizam fiecare valoare pe care o poate lua a, astfel  avem 3 cazuri:

• Cazul 1

a = 7  ⇒ b > 4 ⇒ b ∈ {5, 6, 7, 8, 9} ⇒

$\bf \overline{a5b} \in\{755,756,757,758,759\}$ ⇒

$\bf \overline{ab} \in\{75,76,77,78,79\}\implies\text{\it 5 numere}$

• Cazul 2

a = 8  ⇒ b ∈ {0,1,2,3,4,5,6,7,8,9} ⇒

$\bf \overline{a5b} \in\{850,851,852,853,854,855,856,857,858,859\}$ ⇒

$\bf \overline{ab} \in\{80,81,82,83,84,85,86,87,88,89\}\implies\text{\it 10 numere}$

• Cazul 3

a = 9  ⇒ b ∈ {0,1,2,3,4,5,6,7,8,9} ⇒

$\bf \overline{a5b} \in\{950,951,952,953,954,955,956,957,958,959\}$ ⇒

$\bf \overline{ab} \in\{90,91,92,93,94,95,96,97,98,99\}\implies\text{\it 10 numere}$

Din cele trei cazuri analizate avem:

5 + 10 + 10 = 25 de numere de forma $\bf \overline{ab}$ care respecta conditiile problemei

$\bf \overline{ab} \in\{{75,76,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99\}$

==pav38==