Question

rezolvați ecuația: |13-|2x-7||=16

Answer 1

Răspuns:

S={-11;18}

Explicație pas cu pas:

13-|2x-7|=16

13-16=|...|

-3=|...| x∈∅ pt. ca  |orice|≥0 si -3<0

13-|2x-7|=-16

13+16=|2x-7|

|2x-7|=29

2x-7=29.........2x=36....x=18

2x-7=-29..2x=-22...x=-11

S={-11;18}

Answer 2

$\it |13-|2x-7||=16 \Leftrightarrow 13-|2x-7|=\pm16 \Leftrightarrow 13-|2x-7|\in\{-16,\ 16\}|_{-13} \Leftrightarrow\\ \\\Leftrightarrow -|2x-7| \in \{-29,\ \ 3\}\ \ \ \ \ (1)\\ \\ -|2x-7|\leq0\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow -|2x-7|=-29|_{\cdot(-1)} \Rightarrow |2x-7|=29 \Rightarrow 2x-7=\pm29\Rightarrow \\ \\ \Rightarrow2x-7\in\{-29,\ 29\}|_{+7} \Rightarrow 2x \in \{-22,\ \ 36\}|_{:2} \Rightarrow x \in \{-11,\ \ 18\}$