Question

||x-2|-4|=6
|5-|2x+1||=8
urgent va rog!!!!

Answer 1

||x-2|-4|=6
1) |x-2|-4=6
|x-2|=10
x-2=10
x=12
x-2=-10
x=-8
2) |x-2|-4=-6
|x-2|=-2
x∈∅(multimea vida, adica nici un element, deoarece modulul unui numar este doar pozitiv)
S={-8;12}

|5-|2x+1||=8
1) 5-|2x+1|=8
|2x+1|=-3
x∈∅
2) 5-|2x+1|=-8
|2x+1|=13
2x+1=13
2x=12
x=6
2x+1=-13
2x=-14
x=-7
S={-7; 6}
Sper ca te-am ajutat!
Succes! ;D

Answer 2

[tex]\it||x-2|-4|=6 \\\;\\ \it \ Notam\ |x-2|=y,\ \ y\geq 0 \\\;\\ \it Ecuatia devine: [/tex]

$\it|y-4| =6 \Longrightarrow y-4=\pm6 \\\;\\ y-4=-6 \Longrightarrow y=-6+4 \Longrightarrow y=-2 \ \textless \ 0 \ (nu\ convine) \\\;\\ y-4= 6 \Longrightarrow y= 6+4 \Longrightarrow y = 10 \\\;\\ \it Revenim\ asupra\ notatiei : \\\;\\ \it|x-2|=10 \Longrightarrow x-2=\pm10 \\\;\\ x-2=-10 \Longrightarrow x=-10+2 \Longrightarrow x = -8 \\\;\\ x-2=10 \Longrightarrow x=10+2 \Longrightarrow x=12\ .$

[tex]\it Multimea \ solutiilor\ este : \\\;\\ S\ =\ \{-8,\ 12\}[/tex]