Question

Determinati numerele reale x care verifica egalitatea
a) |x-3|=5
b) ||x-3|-3|=5

c) |||x-3|-3|-3|=5
Ofer 25 de puncte si coroana

Answer 1

a)|x-3|=5

x-3=5=>x=5+3=8

x-3=-5=>x=-5+3=-2

$= > x_{1} = - 2 \\ \\ \: \: \: \: \: \: \: \: \: x_{2} = 8$

b)||x-3|-3|=5

|x-3|-3=5

|x-3|-3=-5

|x-3|=5+3=8

x-3=8=>x=11

x-3=-8=>x=-5

|x-3|=-5+3=-2=>x € ∅

$= > x_{1} = - 5 \\ \\ \: \: \: \: \: \: \: x_{2} = 11$

c)|||x-3|-3|-3|=5

||x-3|-3|=5

||x-3|-3|=-5

||x-3|-3|=5+3=8

|x-3|-3=8=>x=14,x=-8

|x-3|-3=-8=>x € ∅

||x-3|-3|=-5+3=-2=>x € ∅

$= > x_{1} = - 8 \\ \\ \: \: \: \: \: \: \: \: x_{2} = 14$