Question

 Resolva as equações: a)2x²−5x−3=0
b)–2x² +3x+5=0
c) x²−4x+4=0
d) x²+3√2x+4,5=0
e) 4x−x(x−4)=−9 


me ajudem por favor ​

Answer 1

Explicação passo-a-passo:

a) 2x² - 5x - 3 = 0

coeficientes:

a = 2 ; b = - 5 ; c = - 3

x = - b ± √b² - 4ac/2a

x = - (-5) ± √(-5)² - 4.2.(-3)/2.2

x = 5 ± √25 + 24/4

x = 5 ± √49/4

x = 5 ± 7/4

x' = 5+7/4 = 12/4 = 3

x" = 5-7/4 = - 2/4 = - 1/2

S = {- 1/2 ; 3}

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b) - 2x² + 3x + 5 = 0

coeficientes:

a = - 2 ; b = 3 ; c = 5

x = - b ± √b² - 4ac/2a

x = - 3 ± √3² - 4.(-2).5/2.(-2)

x = - 3 ± √9 + 40/-4

x = - 3 ± √49/-4

x = - 3 ± 7/-4

x' = -3+7/-4 = 4/-4 = - 1

x" = -3-7/-4 = -10/-4 = 5/2

S = {- 1 ; 5/2}

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c) x² - 4x + 4 = 0

coeficientes:

a = 1 ; b = -4 ; c = 4

x = - b ± √b² - 4ac/2a

x = - (-4) ± √(-4)² - 4.1.4/2.1

x = 4 ± √16 - 16/2

x = 4 ± √0/2

x = 4 ± 0/2

x = 4/2

x = 2

S = {2}

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d) x² + 3√2x + 4,5 = 0

coeficientes:

a = 1 ; b = 3√2 ; c = 4,5

x = - b ± √b² - 4ac/2a

x = - (3√2) ± √(3√2)² - 4.1.4,5/2.1

x = - 3√2 ± √3.3.2 - 18/2

x = - 3√2 ± √18 - 18/2

x = - 3√2 ± √0/2

x = - 3√2 ± 0/2

x = - 3√2/2

S = {- 3√2/2}

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e) 4x - x.(x - 4) = - 9

4x - x² + 4x = - 9

- x² + 8x + 9 = 0

coeficientes:

a = - 1 ; b = 8 ; c = 9

x = - b ± √b² - 4ac/2a

x = - 8 ± √8² - 4.(-1).9/2.(-1)

x = - 8 ± √64 + 36/-2

x = - 8 ± √100/-2

x = - 8 ± 10/-2

x' = -8+10/-2 = 2/-2 = - 1

x" = -8-10/-2 = -18/-2 = 9

S = {- 1 ; 9}