Question

Stabiliti valoarea de adevar a urmatoarelor propozitii:
a)$\sqrt{2 \sqrt{3} + 2 } * \sqrt{2 \sqrt{3}-2 } apartine Q$

Answer 1

$\sqrt{2 \sqrt{3}+2} \cdot \sqrt{2 \sqrt{3}-2}= \\ \\ =\sqrt{(2 \sqrt{3}+2)(2 \sqrt{3}-2)}= \\ \\ = \sqrt{(2 \sqrt{3})^2-2^2}= \\ \\ = \sqrt{12-4}= \\ \\ = \sqrt{8} \notin Q. \\ \\ Propozitia~este~\underline{falsa}.$