Question

Escreva cada uma das seguintes equações do 2° grau na forma normal reduzida.
a) (x+3)²=1
b) (x-5)²=1
c) (2x-4)²=0
d) (x-3)²= -2x²
e) x²+3x-28=0
f) 3x²-4x+2=0
g) x²-3=4x+2
h) 4x²+9=12x
i) x²=x+12
j) 2x²=-12x-18
k) x²+9= 4x
l) 25x²=20x-4

Answer 1

a)
(x + 3)² = 1
x² + 2.3x + 3² = 1
x² + 6x + 9 = 1
x² + 6x + 9 - 1 = 0
x² + 6x + 8 = 0

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b)
(x - 5)² = 1
x² - 2.5x + 5² = 1
x² - 10x + 25 = 1
x² - 10x + 25 - 1 = 0
x² - 10x + 24 = 0

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c)
(2x - 4)² = 0
(2x)² - 2.4.2x + 4² = 0
4x² - 16x + 16 = 0  (:4)
x² - 4x + 4 = 0

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d)
(x - 3)² = - 2x²
x² - 2.3x + 3² = - 2x²
x² - 6x + 9 = - 2x²
x² + 2x² - 6x + 9 = 0
3x² - 6x + 9 = 0 (:3)
x² - 2x + 3 = 0

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e) já está
x² + 3x - 28 = 0

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f) já está
3x² - 4x + 2 = 0

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g)
x² - 3 = 4x + 2
x² - 4x - 3 - 2 = 0
x² - 4x - 5 = 0

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h)
4x² + 9 = 12x
4x² - 12x + 9 = 0

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i)
x² = x + 12
x² - x - 12 = 0

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j)
2x² = - 12x - 18
2x² + 12x + 18 = 0  (:2)
x² + 6x + 9 = 0

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k)
x² + 9 = 4x 
x² - 4x + 9 = 0

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l)
25x² = 20x - 4
25x² - 20x + 4 = 0