Question

Calculati
$|x - \sqrt{3} | + |x + \sqrt{3} |$
,stiind ca x apartine |R
|x| mai mic sau egal ca
$\sqrt{3}$
​

Answer 1

$\it |x|\leq\sqrt3 \Rightarrow -\sqrt3\leq x\leq\sqrt3|\\ \\ -\sqrt3\leq x\leq\sqrt3|_{-\sqrt3} \Rightarrow -2\sqrt3\leq x-\sqrt3\leq0 \Rightarrow |x-\sqrt3|=-x+\sqrt3\\ \\ -\sqrt3\leq x\leq\sqrt3|_{+\sqrt3} \Rightarrow 0\leq x+\sqrt3\leq2\sqrt3 \Rightarrow |x+\sqrt3|=x+\sqrt3$

Expresia din enunț devine:

$\it -x+\sqrt3+x+\sqrt3=2\sqrt3$

Answer 2

Răspuns:

Explicație pas cu pas:

Conditia initiala  : -√3≤x≤√3

⇒x-√3≤0  ⇒Ix-√3I=-x+√3

-√3≤x  ⇒x+√3≥0  ⇒Ix+√3I=x+3

E=Ix-√3I+Ix+√3I=-x+√3+x+√3=2√3