Para quem ama matematica....
a) x(x+3) - 40=0
b) 10+x(x-2) = 2
c) 4+x(x-4) =x
d) x(x+5) -2x = 28
Respostas
x² + 3x - 40 = 0
a = 1 b = + 3 c = - 40
Δ = b² - 4.a.c
Δ = (3)² - 4.(1).(- 40)
Δ = 9 + 160
Δ = 169
x = [-
b ± √Δ]/2.a
x = [- (+ 3) ± √169]/2.1
x = [ - 3 ± 13]/2
x'= [- 3 + 13]/2 = 10/2
= 5
x"= [ - 3 - 13]/2 = - 16/2
= - 8
S:{- 8 ; 5}
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b) 10+x(x-2) = 2
10 + x² - 2x = 2
x² - 2x + 10 - 2 = 0
x² - 2x + 8 = 0
a = 1 b = - 2 c = + 8
Δ = b² - 4.a.c
Δ = (- 2)² - 4.(1).(+ 8)
Δ = 4 - 32
Δ = - 28 delta negativo, não tem raiz real .
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c) 4+x(x-4) =x
4 + x² - 4x = x
x² - 4x - x + 4 = 0
x² - 5x + 4 = 0
a = 1 b = - 5 c = + 4
Δ = b² - 4.a.c
Δ = (- 5)² - 4.(1).(+ 4)
Δ = 25 - 16
Δ = 9
x = [- b ± √Δ]/2.a
x = [- (- 5) ± √9]/2.1
x = [ + 5 ± 3]/2
x'= [5 + 3]/2 = 8/2 = 4
x"= [5 - 3]/2 = 2/2 = 1
S:{1; 4}
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d) x(x+5) -2x = 28
x² + 5x - 2x - 28 = 0
x² + 3x - 28 = 0
a = 1 b= + 3 c = - 28
Δ = b² - 4.a.c
Δ = (3)² - 4.(1).(- 28)
Δ = 9 + 112
Δ = 121
x = [- b ± √Δ]/2.a
x = [- (+ 3) ± √121]/2.1
x = [ - 3 ± 11]/2
x'= [- 3 + 11]/2 = 8/2 = 4
x"= [ - 3 - 11]/2 = - 14/2 = - 7
S:{- 7 ; 4}