Question

1. Resolva algumas equações:

a) x 2 =16
b) x 2 =81
c) x 2 =5
d) (x+3)2 =25
e) (2x−1) 2 =9
f) (x−5) 2 =7
g) 3x2 -7=5
h) 2x 2 – 13 =5​

Answer 1

Resposta:

Explicação passo a passo:

1. Resolva algumas equações:

a) x^2 = 16

x = \/16

x = +/- 4

R.:

x' = 4

x " = - 4

___________

b) x^2 = 81

x = \/81

x = +/- 9

R.:

x ' = + 9

x" = - 9

__________

c) x^2 =5

x = \/5

R.:

X' = + \/5

x" = - \/5

_____________

d) (x+3)^2 =25

x^2 + 2.3.x + 9 = 25

x^2 + 6x + 9 = 25

x^2 + 6x + 9 - 25 = 0

x^2 + 6x - 16 = 0

a = 1; b = 6, c = - 16

/\= b^2 - 4ac

/\= 6^2 - 4.1.(-16)

/\= 36 + 64

/\= 100

\/ /\= 10

x = ( - b +/- \/ /\)/ 2a

x = [ - 6 +/- 10] / 2.1

x = [ - 6 +/- 10] / 2

x' = ( - 6 + 10)/2 = 4/2= 2

x" = (- 6 - 10)/2 = - 16/2= - 8

R.: v = {2; - 8}

_______________

e) (2x−1)^2 =9

4x^2 - 2.1.2x + 1 = 9

4x^2 - 4x + 1 - 9 = 0

4x^2 - 4x - 8 = 0 (:4)

x^2 - x - 2 = 0

a = 1; b = - 1; c = - 2

/\= b^2 - 4ac

/\= (-1)^2 - 4.1.(-2)

/\= 1 + 8

/\= 9

\/ /\ = \/9 = 3

X = ( - b +/- \/ /\] / 2a

X = [-(-1) +/- 3]/2.1

x = (1 +/- 3]/2

x ' = (1+3)/2 = 4/2 = 2

x " = (1-3)/2 = -2/2= - 1

R.: { 2, - 1}

__________

f) (x−5)^2 =7

x^2 - 2.5.x + 25 = 7

x^2 - 10x + 25 - 7 = 0

x^2 - 10x + 18 = 0

a = 1; b = - 10; c = 18

/\= b^2 - 4ac

/\= (-10)^2 - 4.1.18

/\= 100 - 72

/\= 28

\/ /\= \/28 = \/4.\/7 = 2\/7

x = [ - b +/- \/ /\] / 2a

x = [- (-10) +/- \/28] / 2.1

x = [ 10 +/- 2 \/7] / 2

x = [10/2 +/- 2\/7/2]

R.:

x' = (5 + \/7)

x " = (5 - \/7)

_________

g) 3x^2 - 7 = 5

3x^2 = 5+7

3x^2 = 12

x^2 = 12/3

x^2 = 4

x = \/4

x = +/- 2

R.:

x ' = + 2

x" = - 2

____________

h) 2x^2 – 13 = 5​

2x^2 = 5+13

2x^2 = 18 (:2)

X^2 = 9

X = +/- 3

R.:

x' = + 3

x" = - 3

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