Exercícios de módulo!

Exercícios:

a) | x-3|= 5
x-3=-5
x= -2

x-3= 5
x=8

S= {-2, 8}

b)| x² + 6x - 1|= 6
x²+ 6x-1= -6
x²+ 6x+5=0
S= -6
P= 5
S= {-1,-5}

x²+ 6x-1= 6
x²+6x-7 = 0
S= -6
P = -7
S= {1, -7}

c) | x-x-1|= 1
x²-x-1=-1
x²-x-2=0
S= 1
P= -2
S={-1,2}


x²-x-1=1
x²-x=0
S= 1
P=0
S={0,1}

S={-1,0,1,2}

d) | 2x-5|=x+4
x+4 > 0
x > -4
2x-5 = x+4
x=9

2x-5= -(x+4)
2x-5= -x-4
3x=1
x= 1/3

S= {1/3, 9}

e) |-2x+1|= x+2
x+2 > 0
x> -2
-2x+1= x+2
-3x=1 . (-1)
x= -1/3

-2x+1= -(x+2)
-2x+1= -x-2
-x=-3
x=3

S= { -1/3, 3}

f) |x|- |x|-20=0
|x|= y
y²-y-20=0
S=1
P= -20
S={-4,5}

S={-1,+1,-5,+5}


g) |x|²-3 |x| + 2= 0
|x|= y
y²-3y+2=0
S=3
P=2
S={1,2}