Question

Resolva as equações do 2º grau. com (cálculos) a) x2– 6x + 8 = 0 b) x2 - 5x + 6 = 0 c) x2 -7x+10=0 d) x2- 2x + 1 = 0 e) x2– 4x – 5 = 0 f) x2+ 5x + 6 = 0 g) x2+ 2x – 8 = 0 URGENTE COM CÁLCULOS POR FAVOR !

Answer 1

Oie, Td Bom?!

■ Resolvendo por fatoração.

a)

$x {}^{2} - 6x + 8 = 0$

$x {}^{2} - 2x - 4x + 8 = 0$

$x \: . \: (x - 2) - 4(x - 2) = 0$

$(x - 2) \: . \: (x - 4) = 0$

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$x - 2 = 0⇒x = 2$

$x - 4 = 0⇒x = 4$

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$S = \left \{ 2 \: , \: 4\right \}$

b)

$x {}^{2} - 5x + 6 = 0$

$x {}^{2} - 2x - 3x + 6 = 0$

$x \: . \: (x - 2) - 3(x - 2) = 0$

$(x - 2) \: . \: (x - 3) = 0$

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$x - 2 = 0⇒x = 2$

$x - 3 = 0⇒x = 3$

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$S= \left \{ 2 \: , \: 3 \right \}$

c)

$x {}^{2} - 7x + 10 = 0$

$x {}^{2} - 2x - 5x + 10 = 0$

$x \: . \: (x - 2) - 5(x - 2) = 0$

$(x - 2) \: . \: ( x - 5) = 0$

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$x - 2 = 0⇒x = 2$

$x - 5 = 0⇒x = 5$

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$S = \left \{ 2 \: , \: 5\right \}$

d)

$x {}^{2} - 2x + 1 = 0$

$x {}^{2} - 2 \: . \: x \: . \: 1 + 1 {}^{2} = 0$

$(x - 1) {}^{2} = 0$

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$x - 1 = 0⇒x = 1$

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$S = \left \{ 1\right \}$

e)

$x {}^{2} - 4x - 5 = 0$

$x {}^{2} + x - 5x - 5 = 0$

$x \: . \: (x + 1) - 5(x + 1) = 0$

$(x + 1) \: . \: (x - 5) = 0$

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$x + 1 = 0⇒x = - 1$

$x - 5 = 0⇒x = 5$

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$S= \left \{ - 1 \: , \: 5 \right \}$

f)

$x {}^{2} + 5x + 6 = 0$

$x {}^{2} + 3x + 2x + 6 = 0$

$x \: . \: (x + 3) + 2(x + 3) = 0$

$(x + 3) \: . \: (x + 2) = 0$

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$x + 3 = 0⇒x = - 3$

$x + 2 = 0⇒x = - 2$

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$S= \left \{ - 3 \: , \: - 2 \right \}$

g)

$x {}^{2} + 2x - 8 = 0$

$x {}^{2} + 4x - 2x - 8 = 0$

$x \: . \: (x + 4) - 2(x + 4) = 0$

$(x + 4) \: . \: (x - 2) = 0$

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$x + 4 = 0⇒x = - 4$

$x - 2 = 0⇒x = 2$

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$S= \left \{ - 4 \: , \: 2 \right \}$

Att. Makaveli1996