Ecuatii urgeeent

Natalia Mier Apr 25, 2012 3:05 am

Va rooog intrati in seara asta pe site si aratati-mi si mie rezolvarea la acest punct:
$\left | x^{2}-36 \right | + |6-x|=0$

**Admin** Mier Apr 25, 2012 5:06 am

Rezolvarea standard ar fi :
$\begin{gathered} \left| {{x^2} - 36} \right| + \left| {6 - x} \right| = 0 \hfill \\ \left| {{x^2} - 36} \right| = \left\{ \begin{gathered} {x^2} - 36,{x^2} - 36 \geqslant 0 \hfill \\ - \left( {{x^2} - 36} \right),{x^2} - 36 < 0 \hfill \\ \end{gathered} \right. \Leftrightarrow \left\{ \begin{gathered} {x^2} - 36,{x^2} \geqslant 36 \hfill \\ - \left( {{x^2} - 36} \right),{x^2} < 36 \hfill \\ \end{gathered} \right. \Leftrightarrow \left\{ \begin{gathered} {x^2} - 36,x \in \left( { - \infty , - 6} \right] \cup \left[ {6,\infty } \right) \hfill \\ - \left( {{x^2} - 36} \right),x \in \left( { - 6,6} \right) \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}$
$\begin{gathered} \left| {6 - x} \right| = \left\{ \begin{gathered} 6 - x,6 - x \geqslant 0 \hfill \\ - \left( {6 - x} \right),6 - x < 0 \hfill \\ \end{gathered} \right. \Leftrightarrow \left\{ \begin{gathered} 6 - x,x \leqslant 6 \hfill \\ - \left( {6 - x} \right),x > 6 \hfill \\ \end{gathered} \right. \Leftrightarrow \left\{ \begin{gathered} 6 - x,x\left( { - \infty ,6} \right] \hfill \\ - \left( {6 - x} \right),x > \left( {6,\infty } \right) \hfill \\ \end{gathered} \right. \hfill \\ {\text{Caz 1:}}x \in \left( { - \infty , - 6} \right] - - - - {\text{ecuatia devine :}} \hfill \\ {x^2} - 36 + 6 - x = 0 \Rightarrow ... \Rightarrow x \in \Phi \hfill \\ {\text{Caz 2:}}x \in \left( { - 6,6} \right) - - - - {\text{ecuatia devine}} \hfill \\ \end{gathered}$
$\begin{gathered} - \left( {{x^2} - 36} \right) + 6 - x = 0 \Rightarrow ...x \in \Phi \hfill \\ {\text{Caz 3:}}x \in \left[ {6,\infty } \right) - - - - {\text{ecuatia devine}} \hfill \\ {x^2} - 36 - \left( {6 - x} \right) = 0 \Rightarrow ...x \in 6 \in \left[ {6,\infty } \right) \hfill \\ {\text{Solutie unica }}x = 6 \hfill \\ \end{gathered}$
Sper ca veți deduce pași intermediar , pași ce nu i-am dezvoltat în rezolvare.

Ecuatii urgeeent

Ecuatii urgeeent

Re: Ecuatii urgeeent