Question

Explicitati modulul:a)I4-3√3I=b)I3-2√2I=.

Answer 1

1) I4-3√3I=?

$4-3 \sqrt{3}\ \textless \ 0|+3\sqrt{3}\Rightarrow 4 \ \textless \ 3\sqrt{3}|* \sqrt{3} \Rightarrow 4 \sqrt{3} \ \textless \ 9$

Dupa relatia urmatoare care este adevarata, verificam daca cea de sus este adevarata:

[tex] \sqrt{3}\ \textless \ \sqrt{4} \Rightarrow \sqrt{3}\ \textless \ 2|*4 \Rightarrow4 \sqrt{3}\ \textless \ 8\ \textless \ 9(A)[/tex]

=> 4-3√3<0 =>|4-3√3| = 3√3-4

2) I3-2√2I=?

[tex]3-2 \sqrt{2}\ \textless \ 0|+2\sqrt{2}\Rightarrow 3 \ \textless \ 2\sqrt{2}|* \sqrt{2} \Rightarrow 3 \sqrt{2} \ \textless \ 4| [/tex]

Plecam de la urmatoare relatie care este adevarata si verificam daca cea de sus e adevarata:

$\sqrt{2}\ \textless \ \sqrt{4} \Rightarrow \sqrt{2} \ \textless \ 2|*3 \Rightarrow 3\sqrt{2} \ \textless \ 6 \ \textless\ 4 (F)$

Deci: 3-2√2 > 0 => |3-2√2| = 3-2√2