Question

Determinati numerele naturale a si b astfel incat (a+2)*(b-3)=28

Answer 1

Răspuns: $\red{\bf S(a,b)\in \big\{(26,4);(0,17);(12,5);(2,10);(5,7)\big\}}$

Explicație pas cu pas:

(a + 2) · (b - 3) = 28

Avem o înmulțire de două paranteze, iar pe 28 îl putem scrie ca o înmulțire de două numere astfel:

28 = 1 · 28

     = 28 · 1

     = 2 · 14

     = 14 · 2

     = 7 · 4

$\bf I) ~~(a + 2)\cdot(b - 3) = 1\cdot28$

$\bf a + 2 = 1\Rightarrow a = 1-2~~~Nu ~convine$

$\bf b-3=28\Rightarrow b=28+3\Rightarrow b=31$

$\bf II) ~~(a + 2)\cdot(b - 3) = 28\cdot1$

$\bf a + 2 = 28\Rightarrow a = 28-2\Rightarrow\purple{\underline{a = 26}}$

$\bf b-3 = 1\Rightarrow b = 1+3\Rightarrow\purple{\underline{b = 4}}$

$\bf III) ~~(a + 2)\cdot(b - 3) = 2\cdot14$

$\bf a + 2 = 2\Rightarrow a = 2-2\Rightarrow\purple{\underline{a = 0}}$

$\bf b-3 = 14\Rightarrow b = 14+3\Rightarrow\purple{\underline{b = 17}}$

$\bf IV) ~~(a + 2)\cdot(b - 3) = 14\cdot2$

$\bf a + 2 = 14\Rightarrow a = 14-2\Rightarrow\purple{\underline{a = 12}}$

$\bf b-3 = 2\Rightarrow b = 2+3\Rightarrow\purple{\underline{b = 5}}$

$\bf IV) ~~(a + 2)\cdot(b - 3) = 4\cdot7$

$\bf a + 2 = 4\Rightarrow a = 4-2\Rightarrow\purple{\underline{a = 2}}$

$\bf b-3 = 7\Rightarrow b = 7+3\Rightarrow\purple{\underline{b = 10}}$

$\bf VI) ~~(a + 2)\cdot(b - 3) = 7\cdot4$

$\bf a + 2 = 7\Rightarrow a = 7-2\Rightarrow\purple{\underline{a = 5}}$

$\bf b-3 = 4\Rightarrow b = 4+3\Rightarrow\purple{\underline{b = 7}}$

$\red{\boxed{\bf S(a,b)\in \big\{(26,4);(0,17);(12,5);(2,10);(5,7)\big\}}}$

==pav38==

Baftă multă !