Rezolvarea in Q a ecuatiilor

spaikizz Mier Oct 19, 2011 1:49 am

Am si eu o idee ,dar as vrea sa ma asigur.

|x|= 5,1

|x-2|=1

|x-1\5|=0

Shocked

**Admin** Mier Oct 19, 2011 2:26 am

spaikizz a scris:|x|= 5,1

Din definiția modulului putem asuma: $\left| {\rm{x}} \right| = {\rm{5}},{\rm{1}} \Rightarrow x = \pm {\rm{5}},{\rm{1}}$

|x-2|=1

La fel, folosind definiția modulului :
$\begin{array}{l} \left| {{\rm{x}} - {\rm{2}}} \right| = {\rm{1}}\\ \left| {{\rm{x}} - {\rm{2}}} \right| = \left\{ \begin{array}{l} {\rm{x}} - {\rm{2}} \ge 0,\,\,x \in \left[ {2,\infty } \right)\\ {\rm{ - }}\left( {{\rm{x}} - {\rm{2}}} \right) < 0,\,\,x \in \left( { - \infty ,2} \right) \end{array} \right.\\ {\rm{Caz 1: }}x \in \left[ {2,\infty } \right)\\ \left| {{\rm{x}} - {\rm{2}}} \right| = {\rm{1}} \Leftrightarrow {\rm{x}} - {\rm{2}} = 1 \Rightarrow x = 3 \in \left[ {2,\infty } \right) - - \,\,\left( {ok} \right)\\ {\rm{Caz 2: }}x \in \left( { - \infty ,2} \right)\\ \left| {{\rm{x}} - {\rm{2}}} \right| = {\rm{1}} \Leftrightarrow - \left( {{\rm{x}} - {\rm{2}}} \right) = 1 \Rightarrow x = 1 \in \left( { - \infty ,2} \right)\, - - \,\left( {ok} \right)\\ {\rm{Solutii}}:\,\,x \in \left\{ {1,3} \right\} \end{array}$
Problema 3 analog problemei 2.

Rezolvarea in Q a ecuatiilor

Rezolvarea in Q a ecuatiilor

Re: Rezolvarea in Q a ecuatiilor