Question

determinati numerele rationale a si b daca

Answer 1

Răspuns:

a = 2; b = 1

Explicație pas cu pas:

$a(\sqrt{2} + \sqrt{3}) + b(\sqrt{2} - \sqrt{3}) = \sqrt{18} + \sqrt{2} \\ a \sqrt{2} + a \sqrt{3} + b \sqrt{2} - b \sqrt{3} = 3 \sqrt{2} + \sqrt{2} \\ (a + b) \sqrt{2} + (a - b) \sqrt{3} =3 \sqrt{2} + \sqrt{2}$

→

$\left \{ {{a + b = 3} \atop {a - b = 1}} \right.$

$2a = 4 = > a = 2$

$2 + b = 3 = > b = 1$