Question

Sa se rezolve in R ecuatia |X-1|x|X-2|<6

Answer 1

inecuatia severifica pt x=1 si x=2

tinem cont ca
|a|* |b|=|ab|
atinci
|x²-3x+2|<6

x²-3x+2<6 pt x∈(-∞;1)∪(2;∞)

x²-3x-4<0
x1=-1
x2=4

x∈(-1;4)∩((-∞;1)∪(2;∞))=(-1;1)∪(2;4)

-x²+3x-2<6 pt x∈(1;2)

-x²+3x-8<0
x²-3x+8>0...Δ=9-36<0 adevarta ∀x∈R deci si ∀x∈(1;2)⊂R


atunci x∈(-1;1)∪(2;4)∪{1}∪{2}∪(1;2)=(-1;4)