Question

Rezolvati in Z ecuatiile:
a) -8x+4=-2 la puterea 3
b) -4x=-2 la puterea 4
c) -3x+21=5 la puterea 2 -1
d) modul de x=9
e) modul de x =2
f) modul de x-1 =4
g) modul de x =x
h) modul de x =-x

Answer 1

-8x+4=(-2)³
-8x+4=-8
-8x=-12
x=12/8
x=3/2∉Z Nu se accepta

-4x=(-2)⁴
-4x=16
x=16/(-4)=-4∈Z

-3x+21=5²-1
-3x+21=25-1
-3x+21=24
-3x=24-21
-3x=3
x=3/(-3)=-1∈Z

|x|=9
x=+9; x=-9

|x|=2
x=+2; x=-2

|x-1|=4
x-1=+4; x=5
x-1=-4; x=-3

|x|=x
x=x, orice x∈Z
x=-x; 2x=0; x=0

|x|=-x ; x∈Ф  Nu exista niciun numar real al carui modul sa fie numar negativ.