Question

resolva as equações
a ) 18x-43=63
b) 3(2x-3)+2(x+1)=3x+18
c)2x+3(x-5)=4x+9
d)2(x+1)-3(2x-5)=6x-3
e)x²-x-20=0
f)x²-10x+25=0
g)3x²-15x+12=0

Answer 1

Olá Djjefferson,
Como vai?
Vamos lá:
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A)

18x - 43 = 63
18x = 63 + 43
18x = 106
x = 106 / 18
x = 53 / 9
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B)

3(2x - 3) + 2(x+1) = 3x + 18
6x - 9 + 2x + 1 = 3x + 18
6x + 2x - 3x = 18 + 9 - 1
5x = 26
x = 26 / 5
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C)

2x + 3(x - 5) = 4x + 9
2x + 3x - 15 = 4x + 9
5x - 4x = 9 + 15
x = 24
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D)

2(x + 1) - 3(2x - 5) = 6x - 3
2x + 2 - 6x + 15 = 6x - 3
2x - 6x - 6x = -3 - 2 - 15
-10x = -20 (-1)
x = 20 / 10
x = 2
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E)

x² - x - 20 = 0
Δ = (-1)² - 4·1·(-20)
Δ = 1 + 80
Δ = 81

$x=\frac{-(-1)\pm \sqrt{81}}{2\cdot 1}\to x=\frac{1\pm 9}{2}\\ \\ x'=\frac{10}{2}\to \boxed{x'=5}\\ \\ x''=\frac{-8}{2}\to \boxed{x''=-4}$
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F)

x² - 10x + 25 = 0
Δ = (-10)² - 4·1·25
Δ = 100 - 100
Δ = 0 (delta igual a zero, duas raízes reais e iguais)

$x=\frac{-(-10)\pm \sqrt{0}}{2\cdot 1}\to x=\frac{10\pm 0}{2}\\ \\ x'=\frac{10}{2}\to \boxed{x'=5}\\ \\ x''=\frac{10}{2}\to \boxed{x''=5}$
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G)

3x² - 15x + 12 = 0
Δ = (-15)² - 4·3·12
Δ = 225 - 144
Δ = 81

$x=\frac{-(-15)\pm \sqrt{81}}{2\cdot 3}\to x=\frac{15\pm 9}{6}\\ \\ x'=\frac{24}{6}\to \boxed{x'=4}\\ \\ x''=\frac{6}{6}\to \boxed{x''=1}$
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Espero ter ajudado.