Question

calculati
$\sqrt{(2- \sqrt{5} }) ^{2} + \sqrt{14-6 \sqrt{5} }$

Answer 1

√[(2-√5)^2 ]+√(14-6√5)=√[(2-√5)2]+√[(3-√5)^2]=|2-√5|+|3-√5|
|x|-inseamna modul de x
acum trebuie sa vezi daca ce e in modul e pozitiv sau negativ asta inseamna sa explicitezi modulul.
√5=aproximativ 2.2
√5>2=>|2-√5|=√5-2
3>√5=>|3-√5|=3-√5
Asadar √[(2-√5)^2 ]+√(14-6√5)=√5-2+3-√5=1.

Answer 2

Vom aplica formula:

$\sqrt{x^2}=|x|$

Incercam sa transformam expresia de la al doilea radical:

$14-6\sqrt5=9+5-6\sqrt5=3^2-6\sqrt5+(\sqrt5)^2=(3-\sqrt5)^2$

Expresia data in enunt devine:

[tex]\sqrt{(2-\sqrt5)^2}+\sqrt{(3-\sqrt5)^2}=|2-\sqrt5|+|3-\sqrt5|= -2+\sqrt5+3-\sqrt5 =1[/tex]