Question

resolva as equaçoes do 2 grau imcompletas

a) x²-25x=0
b) x²-25=0
c) 3x²-27=0
d) 27x²-3=0
e) 2x²-1800=0
f)1800x²2x=0

Answer 1

a)
 x² - 25x = 0
x(x - 25) = 0
x = 0

x - 25 = 0
x = 25

R.: x = 0 e x = 25
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b)
 x² - 25 = 0
x² = 25
x = √25
x = +5 e x = - 5
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c)
 3x² - 27 = 0
3x² = 27
x² = 27/3
x² = 9
x = √9
x = + 3 e x = - 3
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d)
 27x² - 3 = 0
27x² = 3 (:3)
9x² = 1
x² = 1/9
x = √1/9
x = +1/3 e x = -1/3
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e)
2x² - 1800 = 0
2x² = 1800
x² = 1800/2
x² = 900
x = √900
x = + 30 e x = - 30
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f)
1800x² - 2x = 0
x(1800x - 2) = 0
x = 0

1800x - 2 = 0
1800x = 2 (:2)
900x = 1
x = 1/900

R.: x = 0 e x = 1/900

Answer 2

a) x² - 25x = 0
    x (x - 25) = 0
    x = 0
    x - 25 = 0 ⇒ x = 25
    S = {0, 25}

b) x² - 25 = 0
    x² = 25
    x = ± √25
    x = ± 5
    S = {-5, 5}

c) 3x² - 27 = 0
    3x² = 27
    x² = 27 / 3
    x² = 9
    x = ± √9
    x = ± 3
    S = {-3, 3}

d) 27x² - 3 = 0
    27x² = 3
    3 (9x² - 1) = 0
    (3x + 1) * (3x - 1) = 0
    3x + 1 = 0 ⇒ 3x = -1 ⇒ x = -1 / 3
    3x - 1 = 0 ⇒ 3x = 1 ⇒ x = 1 / 3
    S = {-¹/₃, ¹/₃}    

e) 2x² - 1800 = 0
    2x² = 1800
    x² = 1800 / 2
    x² = 900
    x = ± √900
    x = ± 30
    S = {-30, 30}

f) 1800x² - 2x = 0
   2x (900x - 1) = 0
   2x = 0 ⇒ x = 0
   900x - 1 ⇒ x = 1 / 900
   S = {0, ¹/₉₀₀}

Espero ter ajudado. Valeu!