Question

Resolva as equações:

a, b, c, d, e

Answer 1

a) x^2 + x = 0
--> x ( x + 1 ) = 0
--> x' = 0
--> x" + 1 = 0 > x" = - 1

b) x (x - 3 ) - 2 ( x - 3 ) = 6
--> x^2 - 3x - 2x + 6 = 6
--> x^2 - 5x + 6 - 6 = 0
--> x^2 - 5x = 0
--> x ( x - 5 ) = 0
--> x' = 0
--> x" -5 = 0 > x" = 5

c) 25x^2 - 20x + 4 = 0
--> a = 25 ; b = - 20 ; c = 4

Formula delta :
D = b^2 - 4 a c
D = (-20)^2 - 4 (25)(4)
D = 400 - 100(4)
D = 400 - 400
D = 0

Foemula de braskara :
x = - b + , - \/D
......________
..............2a

x = - (-20) + , - \/0
......___________
................2(25)

x = 20 + , - 0
......_______
.............50

x' = 20 + 0
......._____
...........50

x' = 20
.......___...(÷10)
........50

x' = 2
.......__
........5

x" = 20 - 0
......._____
...........50

x" = 20
........___..(÷10)
..........50

x" = 2
........__
.........5

C= { 2/5 }

d) 3x^2 + 7x + 3 = x^2 + 2x
--> 3x^2 + 7x + 3 - x^2 - 2x = 0
-->3x^2 - x^2 + 7x - 2x +3 = 0
--> 2x^2 + 5x + 3 = 0
--> a = 2 ; b = 5 : c = 3

Formula delta :
D = b^2 - 4 a c
D = ( 5)^2 - 4 (2) ( 3)
D = 25 - 8(3)
D = 25 - 24
D = 1

Formula de braskara :
x = - b + , - \/D
.......________
................2a

x = -5 + , - \/1
......._______
............2(2)

x = - 5 + , - 1
......._______
...............4

x' = - 5 + 1
......._____
.............4

x' = - 4
.......____
...........4

x' = - 1

x" = - 5 - 1
........._____
...............4

x" = - 6
........____...(÷2)
............4

x" = - 3
........___
...........2

C = { - 3/2 ; -1 }

e) \/x^2 - 3x + 5 = \/2x - 1
--> ( \/x^2 - 3x + 5)^2 = ( \/2x - 1 )^2
--> x^2 - 3x + 5 = 2x - 1
--> x^2 - 3x + 5 - 2x + 1 = 0
--> x^2 - 3x - 2x + 5 + 1 = 0
--> x^2 - 5x + 6 = 0
--> a = 1 ; b = - 5 ; c = 6

Formula delta :
D = b^2 - 4 a c
D = (-5 )^2 - 4(1)(6)
D = 25 - 4 (6)
D = 25 - 24
D = 1

Formula de braskara :
x = - b + ; - \/D
.......________
...............2a

x = - (-5) + ; - \/1
......._________
..............2(1)

x = 5 + ; - 1
......______
............2

x' = 5 + 1
.......____
...........2

x' = 6
.......__
........2

x' = 3

x" = 5 - 1
.......____
...........2

x" = 4
........__
.........2

x" = 2

C = { 2 , 3 }