Question

$Ajutor~,~problema~frumoasa~si~importanta~(pt.mine)~!!! \\ Problema~suna~cam~asa: \\ Cate~elemente~are~multimea: \\ ~A=[x~aparine~Lui~R ~|~|x- \sqrt{3} | ~+~|x- \frac{3}{2} |=x-2] \\ Imi~pare~rau~ca~n-am~pus~paranteze~conform~multimilor~!$

Answer 1

$|x- \sqrt{3}|+|x- \frac{3}{2}| \geq 0. \\ \\ Deci~x-2 \geq 0 \Leftrightarrow x \geq 2. \\ \\ Prin~urmare~x- \sqrt{3}\ \textgreater \ 0,~si~deci ~|x- \sqrt{3}|=x- \sqrt{3}. \\ \\ De~asemenea~x- \frac{3}{2} \ \textgreater \ 0,~si~deci~|x- \frac{3}{2}|=x- \frac{3}{2}. \\ \\ Ecuatia~devine~x- \sqrt{3}+x- \frac{3}{2}=x-2. \\ \\ Va~rezulta~x= \sqrt{3}+ \frac{3}{2}-2. \\ \\ DAR~x \geq 2.~Insa~ \sqrt{3}+ \frac{3}{2}-2\ \textless \ 2+ \frac{3}{2}-2= \frac{3}{2}\ \textless \ 2. \\ \\ Prin~urmare~ecuatia~nu~are~solutii: \\ \\ A= multimea~vida.$