Question

Cum se face asta?
|x+|x-3||=5

Answer 1

$x+|x-3|\in\{5,-5\}$
Avem trei posibilitati:
$a)~x>3\Rightarrow|x-3|=x-3$
$x+x-3=2x-3\in\{5,-5\}$
$2x\in\{8,-2\}$
$x\in\{4,-1\}$
$b)~x=3\Rightarrow|x-3|=0$
$x+0\in\{5,-5\}$
$x\in\{5,-5\}~contradictie$
$c)~x<3\Rightarrow|x-3|=3-x$
$x+3-x\in\{5,-5\}$
$3\in\{5,-5\}~imposibil$