Question

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a)5x^2+13x-10=0

b)8x^2-800=0

c)x^2=0

d)x^2/2+x/9

e)2x^2-x+1=0

f)-9x+x^2=0

Answer 1

a)
5x^2 + 13x - 10 = 0
a = 5; b = 13; c = - 10
∆ = b^2-4ac
∆ = 13^2 - 4.5.(-10)
∆ = 169 + 200
∆ = 369
√∆ = √9.√41
√∆ = 3√41

x = [ - b +/- √∆]/2a
x = [- 13 +/- 3√41]/2.5
x = [ -13 +/- 3√41]/10

x' = [ - 13 - 3√41]/10
x" = [- 13 + 3√41]/10

b)
8x^2-800=0
8x^2 = 800
x^2 = 800/8
x^2 = 100
x = √100
x = +/- 10

R.: (10 ; - 10)

c)
x^2=0
x = 0

R.: { 0 }

d)
x^2/2+x/9 = 0
(9x^2 + 2x)/18 = 0/18
9x^2 + 2x = 0
x.(9x + 2) = 0
x = 0
9x + 2 = 0
9x = - 2
x = - 2/9

R.: {0 , - 2/9}


e)
2x^2 - x + 1 = 0
a = 2; b = - 1; c = 1
∆ = b^2 - 4ac
∆ = (-1)^2 - 4.2.1
∆ = 1 - 8
∆ = - 7
(Não há solução para os números reais, pois ∆ < 0)

f)
- 9x + x^2=0
x^2 - 9x = 0
x.(x - 9) = 0
x = 0
x - 9 = 0
x = 9

R.: {0 , 9}