Question

Calculeaza valoarea expresiei numerice √(√5-2)²+√(√5-3)²

Answer 1

$E= \sqrt{(\sqrt5-2)^2} +\sqrt{(\sqrt5-3)^2} = |\sqrt5-2| + |\sqrt5-3|$

Analizam modulele :

$\sqrt5\ \textgreater \ \sqrt4 \Rightarrow \sqrt5\ \textgreater \ 2 \Rightarrow \sqrt5-2\ \textgreater \ 0\Rightarrow |\sqrt5-2| = \sqrt5-2$

$\sqrt5\ \ \textless \ \ \sqrt9 \Rightarrow \sqrt5\ \textless \ 3 \Rightarrow \sqrt5-3\ \textless \ 0\Rightarrow |\sqrt5-3| = -\sqrt5 +3 = 3-\sqrt5$

Expresia devine:

$E=\sqrt5-2+3-\sqrt5 \ \Longrightarrow\ E = 1.$