Question

Resolva as seguintes equações do 2° grau : 4ײ-27=ײ / K) 8ײ=60 -7ײ / L) 3(ײ-1) = 24 / M) 2(ײ-1) = ײ+7 / N) 5(ײ-1) =4 (ײ+1) / O) (×-3)(×+4)+8=×

Answer 1

• 4x^2 - 27 = x^2
• 4x^2 - 27 - x^2 = 0
• 4x^2 - x^2 - 27 = 0
• 3x^2 - 27 = 0
a = 1 || b = 0 || c = -27
• [-b +/- √(b^2 - 4ac )]/2a
• [0 +/- √(0 - 4 . 1 . (-27))]/2 . 1
• [+/- √(-4 . (-27))]/2
• [+/- √108]/2
• [+/- 6√3]/2
• +/- 3√3
• x1 = +3 // x2 = -3√3

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• 8x^2 = 60 - 7x^2
• 8x^2 - 60 + 7x^2 = 0
• 8x^2 + 7x^2 - 60 = 0
• 15x^2 - 60 = 0
a = 15 || b = 0 || c = -60
• [-b +/- √(b^2 - 4ac)]/2a
• [0 +/- √(0^2 - 4 . 15 . (-60))]/2 . 15
• [+/- √((-60) . (-60))]/30
• [+/- √3600]/30
• [+/- 60]/30
• +/- 2
• x1 = +2 // x2 = -2

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• 3(x^2 - 1) = 24
• 3x^2 - 3 = 24
• 3x^2 - 3 - 24 = 0
• 3x^2 - 27 = 0
a = 3 || b = 0 || c = -27
• [-b +/- √(b^2 - 4ac)]/2a
• [-0 +/- √(0^2 - 4 . 3 . (-27))]/2 . 3
• [+/- √(-12 . (-27))]/6
• [+/- √324]/6
• [ +/- 18]/6
• +/- 3
• x1 = +3 // x2 = -3

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• 2(x^2 - 1) = x^2 + 7
• 2x^2 - 2 = x^2 + 7
• 2x^2 - 2 - x^2 - 7 = 0
• 2x^2 - x^2 - 2 - 7 = 0
• x^2 - 9 = 0
a = 1 || b = 0 || c = -9
• [-b +/- √(b^2 - 4ac)]/2a
• [-0 +/- √(0^2 - 4 . 1 . (-9))]/2 . 1
• [+/- √(-4 . (-9))]/2
• [+/- √36]/2
• [+/- 6]/2
• +/- 3
• x1 = +3 || x2 = -3

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• 5(x^2 - 1) = 4(x^2 + 1)
• 5x^2 - 5 = 4x^2 + 4
• 5x^2 - 4x^2 - 5 - 4 = 0
• x^2 - 9 = 0
a = 1 || b = 0 || c = -9
• [-b +/- √(b^2 - 4ac)]/2a
• [-0 +/- √0^2 - 4 . 1 . (-9))]/2 . 1
• [+/- √(-4 . (-9))]/2
• [+/- √36]/2
• [+/- 6]/2
• +/- 3
• x1 = +3 // x2 = -3

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• (x - 3)(x + 4) + 8 = x
• x^2 + x4 - 3x - 12 + 8 = x
• x^2 + 4x - 3x - 12 + 8 - x = 0
• x^2 + 4x - 3x - x - 12 + 8 = 0
• x^2 + x - x - 20 = 0
• x^2 + (-20) = 0
• x^2 - 20 = 0
a = 1 || b = 0 || c = -20
• [-b +/- √(b^2 - 4ac)]/2a
• [-0 +/- √(0^2 - 4 . 1 . (-20))]/2 . 1
• [+/- √(-4 . (-20))/2
• [+/- √80]/2
• [+/- 4√5]/2
• +/- 2√5
• x1 = +2√5 // x2 = - 2√5