Question

va rog mult e urgent: |1-√5| + {3-√5}

Answer 1

(√5 > 1) => |1-√5| = √5-1

[3-√5]= [3-2,...] = [0,...] = 0 

{3-√5}= 3-√5 -[3-√5] = 3-√5 - 0 = 3-√5


=> |1-√5| + {3-√5} = √5-1+ 3-√5 = 2

Answer 2

[tex]\it \sqrt5\ \textgreater \ \sqrt4=2 \Rightarrow \sqrt5\ \textgreater \ 2|_{\cdot(-1)} \Rightarrow -\sqrt5\ \textless \ -2|_{+1} \Rightarrow \\\;\\ 1-\sqrt5\ \textless \ -1\ \textless \ 0 \Rightarrow |1-\sqrt5| = -1+\sqrt5\ \ \ \ (1)[/tex]

[tex]\it\ Vom\ determina\ \{3-\sqrt5\} \\\;\\ \{3-\sqrt5\} =3-\sqrt5-[3-\sqrt5]\ \ \ \ (2) \\\;\\ Cum\ \sqrt5 \approx 2,23 \Rightarrow 0\ \textless \ 3-\sqrt5\ \textless \ 1 \Rightarrow [3-\sqrt5] =0 \ \ \ (3) \\\;\\ (2),\ (3) \Rightarrow \{3-\sqrt5\} =3-\sqrt5 \ \ \ (4)[/tex]

$\it (1), (4) \Rightarrow |1-\sqrt5| +\{3-\sqrt5\} = -1+\sqrt5+3-\sqrt5 =2$