Question

stabiliti daca numarul n=(√5-2√2)²-(√10-2)²

Answer 1

Formula pe care o vom folosi:
$(a-b)^2=a^2-2ab-b^2$

Asadar calculam numarul si obtinem

$n=5-4 \sqrt{10}+8-(10-4 \sqrt{10}+4)=13-4 \sqrt{10}-10+4\sqrt{10}-4 \\ n=-1\notin N$

Answer 2

$n=( \sqrt{5} -2 \sqrt{2} )^2-( \sqrt{10} -2)^2 \\ n= \sqrt{5} ^2-2* \sqrt{5} *2 \sqrt{2} +(2 \sqrt{2} )^2-( \sqrt{10} ^2-2* \sqrt{10} *2+2^2) \\ n=5-4 \sqrt{10} +8-10+4 \sqrt{10} -4 \\ n=5+8-10-4$
$n=-1$ ∉ $N$