Question

Resolva em R as seguintes equações:
a) (x + 2)² = 2 . (2x +3)

b) (x - 5)² = 2x . (x - 5)

c) 2/5 = 5x²/2

d) 5x² + 7x + 1 = 3x² + 2x + 1

e) (2x - 3) . (x + 4) = (x + 2) . (5x - 6)


PS: Respostas com cálculos, por favor. Obrigada! <3

Answer 1

a.-) ( X - 2)^2 = 2 . ( 2X + 3 )
x^2 - 2(x)(2) + (2)^2 = 4x + 6
x^2 - 4x + 4 = 4x + 6
x^2 - 4x - 5x + 4 - 6 = 0
x^2 - 9x - 2 = 0
a = 1 --- b = - 9 ---- c = - 2

Formula delta :

D = b^2 - 4 a c

D = (- 9)^2 - 4 (1) (-2)

D = 81 - 4 (-2)

D = 81 + 8

D = 89

Formula de braskara :

x = - b + , - \/ D
......_________
...............2a

x = - (-9) + , - \/ 89
.......___________
..................2(1)

x = 9 + , - 9,43
......_________
...............2

x1 = 9 + 9,43
........_______
................2

x1 = 18,43
........_____
.............2

x1 = 9,215

x1 = 9,22
----------------------------
x2 = 9 - 9,43
........_______
...............2

x2 = - 0,43
..........._____
...............2

x2 = - 0,215

x2 = - 0,22

b.-) (X - 5 )^2 = 2x . ( X - 5 )
x^2 - 2(x)(5) + (5)^2 = 2x^2 - 10x
x^2 - 10x + 10 = 2x^2 - 10x
x^2 - 2x^2 - 10x +10x +10 = 0
- x^2 + 10 = 0
- x^2 = - 10..(-1)
x^2 = 10
x = \/ 10

c.-) 2/5 = 5x^2/2
.......2(2) = 5x^2 (5)
.......4 = 25 x^2
.......25 x^2 = 4
.......x^2 = 4 / 25
.......x = \/ 4 / \/ 25
.......x = 2/5

d.-) 5x^2 + 7x + 1 = 3x^2 + 2x + 1
5x^2 - 3x^2 + 7x - 2x + 1 - 1 = 0
2x^2 + 5x = 0
x(2x + 5) = 0
x1 = 0
2x2 + 5 = 0
2x2 = - 5
x2 = - 5/2

e.-) ( 2x - 3 ) . ( x + 4 ) = ( x + 2 ) . ( 5x - 6 )
2x^2 + 8x - 3x - 12 = 5x^2 - 6x + 10x - 12
2x^2 + 5x - 12 = 5x^2 + 4x - 12
2x^2 - 5x^2 +5x - 4x - 12 + 12 = 0
- 3x^2 + x = 0
- x (3x + 1 ) = 0
- x1 =0
x1 = 0
-------------------
3x2 + 1 = 0
3x2 = - 1
x2 = - 1/3