Question

Sa se rezolve ecuatiile:
a) |x|=0
b)|x-3|=1
c)|2x-1|=3

Answer 1

IxI=0  x=0

Ix-3I=1
Ix-3I=x-3 daca x-3>=0 adica x>=3
Ix-3I=-x+3 daca x-3<0 adica x<3
x-3=1, x=1+3, x=4>=3
-x+3=1, x=3-1 x=2<3
Solutiile sunt 2 si 4

|2x-1|=2x-1 daca 2x-1>=0 adica x>=1/2
|2x-1|=-2x+1 daca 2x-1<0 adica x<1/2
2x-1=3, 2x=1+3, 2x=4, x=2>=1/2
-2x+1=3, 2x=1-3, 2x=-2, x=-1<1/2
Solutiile sunt -1si 2