Question

Resolva as equações em R com Calculo e resposta obrigado a)2x² -8x+8=0 b)3x² -7x+2=0 C)x²+9=4x D)2x=15-x² E)3x²+7x+3=x²+2x F)x(x+5)-2x=28 G)(x+3)(x-4)-52=-x H) (1-x²)-3x=1

Answer 1

2x² - 8x + 8 = 0
Delta = b² - 4ac
Delta = 64 - 4(2)(8)
Delta = 64 - 64
Delta = 0
X = (-b +- raiz delta) / 2a
X = (8 +- 0) / 4
x' e x" = 8/4 = 2

===========================

3x² - 7x + 2 = 0
Delta = b² - 4ac
Delta = 49 - 4(3)(2)
Delta = 49 - 24
Delta = 25
X = (-b +- raiz delta) / 2a
X = (7 +- 5) / 6
x' = (7 + 5) / 6 = 12/6 = 2
x" = (7 - 5) / 6 = 2/6 = 1/3

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x² - 4x + 9 = 0
Delta = b² - 4ac
Delta = 16 - 4(1)(9)
Delta = 16 - 36
Delta = -20
Não existe raiz negativa

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x² + 2x - 15 = 0
Delta = b² - 4ac
Delta = 4 - 4(1)(-15)
Delta = 4 + 60
Delta = 64
X = (-b +- raiz delta) / 2a
X = (-2 +- 8) / 2
x' = (-2 + 8) / 2 = 6/2 = 3
x" = (-2 - 8) / 2 = -10/2 = -5

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3x² + 7x + 3 = x² + 2x
3x² - x² + 7x - 2x + 3 = 0
2x² + 5x + 3 = 0 <<<<<<<<<<<<<
Delta = b² - 4ac
Delta = 25 - 4(2)(3)
Delta = 25 - 24
Delta = 1
X = (-b +- raiz delta) / 2a
X = (-5 +- 1) / 4
x' = (-5 + 1) / 4 = -4/4 = -1
x" = (-5 - 1) / 4 = -6/4 = -3/2

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x(x + 5) - 2x = 28
x² + 5x - 2x - 28 = 0
x² + 3x - 28 = 0 <<<<<<<<<
Delta = b² - 4ac
Delta = 9 - 4(1)(-28)
Delta = 9 + 112
Delta = 121
X = (-b +- raiz delta) / 2a
X = (-3 +- 11) / 2
x' = (-3 + 11) / 2 = 8/2 = 4
x" = (-3 - 11) / 2 = -14/2 = -7

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(x + 3)(x - 4) - 52 = - x
x² - 4x + 3x - 12 - 52 = -x
x² - x - 64 + x = 0
x² - 64 = 0
x² = 64
x = raiz 64
x = 8

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(1 - x²) - 3x = 1
1 - x² - 3x - 1 = 0
-x² - 3x = 0 (*-1)
x² + 3x = 0
x(x + 3) = 0
x = 0

x + 3 = 0
x = -3

ESPERO TER TE AJUDADO!