Question

Rezolvati in R:
|x-1|+|x-4|=3

Answer 1

se observa ca pt x=1 si, respectiv pt x=3 ecutia severifica

intr-adevar|1-4|=3 si

|2|+|-1|=3

x∈(-∞;-1)

-x+1-x+4=3

2x=2..x=1∉(-∞;1)

pt x∈(1;3)

x-1-x+4=3..3=3 adevarat ∀x∈(1;4)

x∈(4;∞)

x-1+x-4=3

2x=8

x=4∉(4;∞)

S= {1}∪{4}∪(1;4)=[1;4]