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

Răspuns :

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

Analizam modulele :

[tex]\sqrt5\ \textgreater \ \sqrt4 \Rightarrow \sqrt5\ \textgreater \ 2 \Rightarrow \sqrt5-2\ \textgreater \ 0\Rightarrow |\sqrt5-2| = \sqrt5-2[/tex]

[tex]\sqrt5\ \ \textless \ \ \sqrt9 \Rightarrow \sqrt5\ \textless \ 3 \Rightarrow \sqrt5-3\ \textless \ 0\Rightarrow |\sqrt5-3| = -\sqrt5 +3 = 3-\sqrt5[/tex]

Expresia devine:

[tex]E=\sqrt5-2+3-\sqrt5 \ \Longrightarrow\ E = 1.[/tex]