Question

Aratati ca radical( 5x + 7) nu apartine Q, oricare ari fi x apartine N. Multumesc.

Answer 1

$\sqrt{5x+7}\in\mathbb{Q}\Leftrightarrow5x+7~patrat~perfect$
$u(5x)\in\{0,5\},~\forall x\in\mathbb{N}$
$u(5x+7)\in\{7,2\}$
Daca un numar are ultima cifra 2 sau 7 (sau 3 sau 8) nu este patrat perfect
$Deci~\sqrt{5x+7}\not\in\mathbb{Q}$